AP Physics 2: Algebra-Based FRQ Room

Adjustable Pipe Flow Experiment

In an experiment, water flows through a pipe whose cross-sectional area can be mechanically adjusted

Airflow and Lift on an Aircraft Wing using Bernoulli's Principle

An aircraft wing is designed so that the airspeed over the top surface is 250 m/s and beneath the wi

Airflow and Lift on an Airfoil

An airplane wing is designed so that the air above the wing travels at a different speed than the ai

Airflow over an Airfoil Experiment

A wind tunnel experiment investigates the pressure distribution on an airfoil. Sensors along the cho

Analysis of a Fluid Flow Experiment with a Differential Pressure Sensor

In a horizontal pipe, a differential pressure sensor records the pressure at various measurement poi

Analyzing a High-Speed Water Jet

A garden hose with an initial inner diameter of $$2\;cm$$ is fitted with a nozzle that reduces the d

Bernoulli's Data Analysis

An experiment is conducted where a fluid flows through a horizontal pipe. A graph showing the variat

Bernoulli's Equation in Pipe Flow

A pump forces water through a horizontal pipe that includes a constriction. At Point 1 (just after t

Bernoulli's Principle and Aircraft Lift

Air flows over the upper and lower surfaces of an airplane wing. In a certain section along the wing

Bernoulli's Principle and Airflow Over a Wing

An airplane wing is designed with a curved top and a flatter bottom to create differing air velociti

Bernoulli’s Principle and Pressure Measurements

Water is pumped through a horizontal pipe that constricts and expands in diameter. At Point 1 in the

Buoyancy and Archimedes’ Principle Experiment

An object with a mass of $$150\,kg$$ and a volume of $$0.75\,m^3$$ floats in a fluid of unknown dens

Buoyancy and Floating Object Experiment

An object with a mass of $$150 \; kg$$ and a volume of $$0.75 \; m^3$$ is placed in ethyl alcohol, w

Buoyancy and Floating Objects Analysis

An object with a mass of $$150~kg$$ and volume of $$0.8~m^3$$ is placed in a container filled with a

Buoyancy and Submerged Volume of a Submarine

A submarine with a total volume of 300 m³ is designed to be neutrally buoyant in seawater (density $

Buoyancy Experiment with Incorrect Variable Substitution

A student designs an experiment to determine the fraction of an object's volume that is submerged wh

Buoyant Force and Submerged Volume Analysis

An object with a mass of 150 kg and a volume of 0.75 m³ is observed to float in ethyl alcohol (densi

Buoyant Force Measurement Experiment

In an experiment designed to measure buoyant force, the weights of submerged objects were recorded.

Comparative Analysis of Pressure in Open versus Closed Fluid Systems

Two identical containers are filled with the same fluid. Container A is open to the atmosphere, whil

Continuity Equation and Flow Rate in a Non-Uniform Pipe

Water flows through a pipe whose cross-sectional area changes along its length. At point 1 the pipe

Continuity Equation in a Constricted Pipe Experiment

A student sets up a horizontal pipe with two sections: one wide and one significantly constricted. T

Continuity Equation in a Varying-Diameter Pipe

A fluid flows through a pipe that changes diameter along its length. At Section 1, the pipe has a ra

Coupling Initiation of Flow in a Pipe with Varying Diameter

A horizontal pipe initially at rest is suddenly opened by a valve, leading to fluid flow through a s

Density and Hydrostatic Pressure Calculation

A container holds an oil sample with a measured mass of $$1.6$$ kg and a volume of $$2.00 \times 10^

Density Determination and Fluid Identification

This problem focuses on calculating density and using that result to discuss buoyancy. Answer the fo

Density Determination Experiment

In a laboratory experiment, a student measures the density of an unknown oil sample by determining i

Density Determination Experiment

A researcher is investigating the density of three different fluids in the lab. The aim is to accura

Density Measurement Using a Hydrometer

A hydrometer is an instrument that measures liquid density by floating at a level where the buoyant

Designing a Pipeline: Balancing Pressure and Flow Rate

An engineering project requires designing a pipeline to transport water over long distances. Changes

Designing a Water Distribution System using the Continuity Equation

An engineering water distribution system uses a main pipe which eventually splits into several branc

Dynamic Pressure and Airspeed from Pitot Tube Measurements

A Pitot tube is used on an aircraft to measure dynamic pressure, which is then used to calculate the

Effect of Temperature on Fluid Density and Pressure

A container holds a fluid that is heated from 20°C to 80°C, causing its density to decrease from 100

Energy Conservation in Fluid Flows

Using Bernoulli's equation, derive an expression that relates the change in kinetic energy per unit

Energy Loss and Friction in Extended Pipe Flow

Water is pumped through a long, straight pipe, and energy losses occur due to friction along the pip

Evaluating Fluid Pressure under Variable Density Conditions

In an experimental setup, the fluid density varies with depth according to $$\rho(y) = \rho_0 + k *

Flow Rate and Pipe Constriction

Water flows through a horizontal cylindrical pipe that narrows from a radius of 4.0 cm to a radius o

Flow Rate Variation in a Branching Pipe

A horizontal pipe carrying a total flow rate of $$0.012\,m^3/s$$ splits into two branches. One branc

Fluid Density and Pressure in a Tank

A cylindrical tank contains an unknown fluid. The tank has a height of $$h = 2.0~m$$ and a base area

Fluid Statics in Deep-sea Conditions

A submersible is designed to operate at extreme depths in the ocean. At a depth of $$4000 \cdot m$$

Hydrostatic Pressure in a Liquid Column

Consider an open tank filled with a liquid of density $$\rho$$. The hydrostatic pressure at a depth

Hydrostatic Pressure in an Open Tank

A researcher investigates hydrostatic pressure within an open water tank. The study aims to measure

Hydrostatics in a Multi-Layer Fluid System

A container holds two immiscible liquids arranged in layers. The top layer is oil with density 800 k

Inclined Pipe Flow with Incorrect Gravitational Component

A student analyzes fluid flow in an inclined pipe by measuring pressure at the upper and lower secti

Integrated Fluid Dynamics Investigation

A chemical engineering laboratory examines the behavior of an incompressible fluid (density = $$1000

Investigating Fluid Viscosity Effects on Flow

Fluid viscosity plays a significant role in determining flow characteristics. High viscosity fluids

Investigating Pressure Differences in Fluid Circuits

A U-shaped tube contains a fluid with a density of 1200 kg/m³. A small height difference between the

Investigating Viscosity in Fluid Flow

A researcher explores the effect of fluid viscosity on flow rate through a narrow tube. Two liquids

Lab Analysis: Determining the Density of an Unknown Fluid Using a Jet of Water

In a laboratory experiment, a horizontal jet of water is directed into a shallow container filled wi

Layered Fluid Pressure in an Oil-Water System

A container holds two immiscible fluids. The top layer is oil with a density of $$800\,kg/m^3$$ and

Mapping Fluid Pressure Distribution Using Sensors

Design an experiment to map the pressure distribution within a fluid container by using multiple pre

Multi-Variable Analysis in a Fluid Mixing Problem

A container holds two immiscible liquids: Liquid A (density = 900 kg/m³) forms the top layer and Liq

Pipe Flow and the Continuity Equation Experiment

A student is investigating fluid flow through a pipe whose diameter varies along its length. The hyp

Pipe Flow Dynamics in Constriction

An experiment measures the flow speed of water in different segments of a pipe with varying radii. T

Pressure Distribution in a Fluid at Rest

Consider a tank filled with a liquid of density $$\rho$$. The pressure at a given depth is described

Pump Power in a Multi-Elevation Piping System

A pump moves water (density = 1000 kg/m³) through a piping system where the water is elevated by 2 m

River Flow Dynamics Study

A team of engineers conducts a field study to measure the flow characteristics of a river. They reco

Tank Discharge Flow Experiment

An experiment investigates the discharge of water from a tank through a small orifice at the bottom.

Temperature Effects on Fluid Pressure

Changes in temperature can affect the density of a fluid, and therefore the hydrostatic pressure at

Temperature Effects on Fluid Viscosity and Flow

In an experiment, the flow rate of a viscous fluid through a fixed nozzle is measured at various tem

Temporal Flow Rate Analysis from an Experimental Graph

A student records the flow speed of water through a pipe over a 30-second interval. The graph shows

Turbulent vs. Laminar Flow: Reynolds Number Misinterpretation

A student conducts an experiment to study the transition from laminar to turbulent flow in a pipe by

Adiabatic Process Compression Experiment Error

A student conducts an experiment to study adiabatic compression in a gas contained within a piston-c

Adiabatic vs. Isothermal Transition Timing Experiment Error

A student designs an experiment to compare adiabatic and isothermal expansions of a gas by rapidly m

Analysis of Isothermal Process Cycle Using a P–V Diagram

Isothermal processes occur at constant temperature, and the work done can be determined from a P–V d

Analyzing Energy Balance in a Calorimetry Experiment

In a calorimetry experiment, a water bath is used to measure the energy transfer. The specific heat

Analyzing Work Done in Different Thermodynamic Paths

A gas undergoes changes between states along two alternate paths on a P–V diagram. Path 1 is a const

Conduction, Specific Heat, and Temperature Change

A metal rod of mass 2 kg and specific heat capacity 400 J/(kg·K) is heated by supplying 8000 J of en

Cyclic Heat Engine Efficiency and Work

A cyclic heat engine operates on a simplified cycle consisting of four segments: 1. Isothermal expa

Derivation of the Root Mean Square Velocity

Starting from the average kinetic energy equation $$\frac{1}{2} m(v^2)_{avg} = \frac{3}{2} k_B T$$,

Designing an Experiment to Measure Convective Heat Transfer

A researcher aims to measure the convective heat transfer coefficient in a fluid flowing over a heat

Deviations of Real Gases from Ideal Behavior

The ideal gas law, $$PV = nRT$$, describes gases under ideal conditions. However, at high pressures

Entropy and the Second Law

The Second Law of Thermodynamics introduces the concept of entropy, which is often associated with t

Entropy Change and the Second Law of Thermodynamics

During a reversible isothermal expansion of an ideal gas, the entropy change is described by the equ

Entropy Change in Gas Mixing Experiment

Two chambers, each containing 0.5 moles of an identical ideal gas at 300 K and with a volume of 0.01

Entropy Changes in Thermodynamic Processes

Consider an ideal gas that undergoes an isothermal expansion from an initial volume $$V_1$$ to a fin

Evaluating a Cooling System's Efficiency

A refrigerator extracts 500 J of heat from its interior and requires 150 J of work input per cycle.

Evaluating Experimental Error in the Ideal Gas Law Measurements

A laboratory experiment uses measured values of pressure, volume, and temperature to calculate the n

Exploring Kinetic Molecular Theory via Maxwell-Boltzmann Distribution

An experiment is conducted to study the speed distribution of gas molecules. The data is represented

First Law of Thermodynamics in a Closed System

An experiment on a closed system records the changes in internal energy, heat added, and work done o

Force on Container Lid from Confined Gas

A cylindrical container has a radius of 15 cm and a height of 30 cm. It contains 0.6 moles of an ide

Gas Pressure Calculation and Net Force Analysis

A 0.8 mole sample of an ideal gas is confined in a cubic container with a side length of 0.5 m at a

Heat Conduction in a Metal Rod

A researcher studies heat transfer through a long, homogeneous metal rod that is heated at one end w

Heat Engine Efficiency Analysis

A heat engine operates by drawing heat from a high-temperature source and rejecting part of it as ex

Heat Engine Efficiency and Work Output

A heat engine undergoes a cyclic process where it absorbs 800 J of heat from a high-temperature sour

Heat Engine Efficiency in Different Thermal Reservoir Conditions: Experimental Design

The efficiency of a heat engine depends on the temperatures of its high-temperature and low-temperat

Heat Engines and Maximum Efficiency

No heat engine can achieve 100% efficiency due to inherent energy losses. (a) Explain why complete c

Heat Transfer by Radiation

Unlike conduction and convection, heat transfer by radiation involves electromagnetic waves. (a) Wri

Heating a Gas: Conduction vs. Convection

Heat can be transferred via different mechanisms. In the context of a gas being heated, consider the

Influence of Molar Mass on Molecular Speeds

A researcher compares the root-mean-square speeds of molecules from two different gases under identi

Investigating Pressure-Temperature Relationship in a Closed Gas Container

In a constant-volume container, the pressure of a confined gas changes as the temperature varies. De

Irreversible Processes and Entropy Analysis

A claim is made that during an irreversible process in an isolated system, the total entropy always

Isothermal Process Work Calculation

An ideal gas undergoes an isothermal expansion at a constant temperature of 350 K. The gas expands f

Maxwell-Boltzmann Distribution Analysis

The Maxwell-Boltzmann distribution provides a statistical description of the speeds of molecules in

Maxwell-Boltzmann Distribution Analysis

A researcher claims that increasing the temperature of a gas not only increases the average speed of

Maxwell-Boltzmann Distribution Analysis Experiment Error

A student conducts an experiment to validate the Maxwell-Boltzmann distribution by measuring the fli

Phase Diagrams and Critical Points

Phase diagrams provide insight into the states of a pure substance under various conditions. (a) Des

Pressure Sensor Calibration Error in Gas Experiment

In an experiment intended to verify the Ideal Gas Law, a student uses a pressure sensor to record th

Real vs. Ideal Gas Behavior

While the Ideal Gas Law $$PV = nRT$$ describes the behavior of gases under many conditions, real gas

Testing Thermal Equilibrium: The Zeroth Law

An experiment is conducted to verify the Zeroth Law of Thermodynamics using three objects: A, B, and

Thermal Conductivity through Conduction

An experiment measures the rate of heat transfer through a material using the conduction formula $$\

Thermal Insulation Effectiveness Experiment Error

A student conducts an experiment to test the effectiveness of different insulation materials by meas

Thermodynamic Analysis of an Ice Melting Process

When heat is added to a substance at its melting point, the phase change occurs without a change in

Work in Cyclic Thermodynamic Processes

A researcher analyzes two different cyclic processes shown on P–V diagrams. Process 1 follows a rect

Analysis of Equipotential Maps and Electric Field Lines

Consider a dipole formed by two equal but opposite point charges. Analyze the relationship between e

Balanced Forces: Charged Balloon in Combined Electric and Gravitational Fields

A student sets up an experiment to determine the charge required on a small balloon so that the upwa

Capacitor Energy Storage Experiment

A laboratory experiment investigates the energy stored in a parallel-plate capacitor. In this experi

Capacitor Voltage and Plate Area Calculation

A parallel-plate capacitor holds a charge of $$50\;\mu C$$ on each plate and has a capacitance of $$

Charge Induction on Conductors vs. Insulators

A charged rod is brought near two spheres—one made of a conductor and one made of an insulator—that

Charge Redistribution in Connected Conductors

In a series of experiments, two conducting spheres initially carrying different charges were connect

Comparing Electric and Gravitational Forces in a Hydrogen Atom

A hydrogen atom consists of a proton and an electron separated by a Bohr radius of 0.5 × 10⁻¹⁰ m. Th

Diagram Analysis: Electric Field Lines and Equipotentials in a Dipole

The following diagram represents an electric dipole configuration. It shows two charges located on t

Dielectric Effects on Capacitor Energy

A researcher is studying how the introduction of a dielectric affects the energy stored in a paralle

Dipole Electric Field Analysis

Consider an electric dipole formed by two point charges of equal magnitude $$|Q| = 4.0 \times 10^{-9

Electric Dipole Analysis in a Uniform Medium

An electric dipole is formed by two point charges, +4.0 nC and -4.0 nC, separated by 6.0 cm in air.

Electric Field and Potential of an Infinite Charged Sheet

A very large sheet has a uniform surface charge density σ = 5.0×10^-6 C/m². Answer the following: (a

Electric Field Mapping and Equipotential Surfaces

In an experiment, equipotential maps are generated for a charge configuration. These maps illustrate

Electric Field Mapping in a Non-Uniform Field

A point charge is fixed on an insulating board. A voltage probe is used to measure the electric pote

Electric Field Mapping Using Discrete Data Points

A student conducts an experiment to measure the electric field around a set of point charges by firs

Electric Field Superposition in a Triangular Configuration

Three point charges are fixed at the vertices of an equilateral triangle. A fourth charge is placed

Electric Potential Dependence Experiment

An experiment is conducted to measure the electric potential at various distances from a fixed point

Electric Potential Due to a Point Charge

A point charge of $$+2.0*10^{-9}$$ C creates an electric potential in the surrounding space. (a) Ca

Electric Potential Due to Multiple Charges

Consider two point charges: $$Q_1 = +2 \times 10^{-9} \; C$$ located at \((-0.04 \; m, 0)\) and $$Q_

Electric Potential Measurement Setup: Reference Point Error

An experiment is set up to measure the electric potential around a fixed point charge. A voltmeter i

Electric Potential Variation in a Conical Capacitor

A non-standard capacitor is constructed with one plate conically shaped, leading to non-uniform sepa

Electrostatic Shielding

A researcher investigates the phenomenon of electrostatic shielding by placing a charged rod near a

Energy Storage in a Capacitor with a Dielectric Material

A capacitor with initial capacitance $$C_0$$ is charged to a voltage $$V_0$$. After charging, the ca

Equipotential Surface Analysis in a Dipole Field

This question uses the mapping of equipotential surfaces in the vicinity of an electric dipole to ex

Force Comparison in Hydrogen Atom

An experiment is conceptually designed to compare the magnitude of the electric force to the gravita

Force on Test Charge in a Uniform Electric Field

A test charge of $$+3.0*10^{-9}$$ C is placed in a uniform electric field of magnitude 400 N/C that

Impact of a Dielectric on a Capacitor's Properties

A parallel-plate capacitor with a plate separation of $$1.0\,mm$$ and plate area of $$0.05\,m^2$$ is

Inductive Charging Experiment of Spheres

In an experiment, two identical initially neutral conducting spheres are placed on an insulating sta

Investigating Capacitor Energy Storage Versus Separation Distance

Design an experiment to measure how the energy stored in a parallel-plate capacitor changes as the d

Investigation of the Inverse-Square Law in Electrostatics

An experiment is conducted to verify the inverse-square law for the electric field produced by a poi

Measuring Coulomb Force Experiment

A scientist is investigating the validity of Coulomb's Law by measuring the force between two charge

Millikan Oil Drop Experiment Analysis

The Millikan oil drop experiment played a pivotal role in determining the fundamental charge of the

Motion of a Charged Particle in a Non-Uniform Electric Field

A particle with charge \(q\) and mass \(m\) moves into a region where the electric field varies with

Net Electric Force in a Square Configuration

Four identical positive point charges, each of $$2.0 \times 10^{-9} \; C$$, are placed at the vertic

Net Electric Force on a Central Charge in a Square Configuration

Four equal positive point charges are fixed at the vertices of a square, and a negative point charge

Non-Uniform Charge Distribution Effects

A researcher examines the electric field created by a hemispherical charge distribution with total c

Potential Energy Change in a Non-Uniform Field

Consider a fixed point charge $$Q$$. A test charge $$q$$ moves from a distance $$r_A$$ to $$r_B$$ fr

Proton–Electron Force Comparison in a Hydrogen Atom

In a hydrogen atom the proton and electron are separated by a Bohr radius of 0.5×10^-10 m. Given tha

Square Charge Configuration

A researcher sets up a square configuration in vacuum with four point charges placed at the corners

Vector Addition of Electric Forces in an Equilateral Triangle

Three point charges are placed at the vertices of an equilateral triangle with each side measuring 0

Work Done and Change in Electric Potential Energy

A particle with charge $$q = +3.0 \times 10^{-9} \; C$$ is displaced by $$0.05 \; m$$ in the directi

Advanced Analysis of Battery Internal Resistance with External Loads

A battery with an internal resistance r is connected to various external load resistors. The table b

Analysis of a Circuit with Time-Dependent Current (Transient Response)

In an RC circuit, the current during the charging phase of a capacitor is given by $$I(t) = \frac{V}

Analyzing Energy Dissipation in Circuits with Multiple Components under Variable Loads

A study claims that by optimizing the configuration of resistor networks, overall energy dissipation

Analyzing Power Dissipation with a Variable Resistor

A resistor with a variable resistance ranging from 5 Ω to 20 Ω is connected to a constant 12 V sourc

Analyzing Power Efficiency in Batteries with Internal Resistance

A battery with an EMF of 15 V and internal resistance $$r = 0.5\,Ω$$ is connected to a load resistor

Application of Kirchhoff’s Junction and Loop Rules

Consider a circuit where three branches intersect at a junction. Two branches carry currents $$I_1$$

Application of Kirchhoff’s Laws in Complex Circuits

Consider a circuit that has two branches: one branch contains a single resistor and the other branch

Assessing Charging Curves of Capacitors in Series and Parallel

An experiment claims that the charging curves of capacitors differ based on whether they are arrange

Battery and Capacitor in Renewable Energy Applications

In a simplified model of a solar panel energy storage system, a battery with an ideal EMF of 18 V an

Battery Internal Resistance Analysis

A battery with an electromotive force $$\varepsilon = 12\,V$$ and internal resistance $$r = 1\,\Omeg

Battery Internal Resistance Analysis

A battery can be modeled as an ideal EMF in series with an internal resistance r. The following tabl

Battery Internal Resistance and Terminal Voltage

A battery can be modeled as an ideal EMF in series with an internal resistance. Consider a battery w

Capacitor Charging Experiment in an RC Circuit

A student assembles an RC circuit that includes a 12 V battery, a 3 Ω resistor, and an initially unc

Capacitor Discharging Analysis

A fully charged 12 V capacitor in an RC circuit is allowed to discharge through a resistor. The volt

Circuit Analysis with Multiple Voltage Sources

A circuit contains two batteries with EMFs of 12 V and 9 V connected in opposition (i.e., the positi

Circuit Simulation Verification

An experiment is conducted to compare the theoretical predictions of a circuit simulation with actua

Current Flow Analysis in a Simple Battery Circuit

A researcher claims that a circuit composed of a 12 V battery and various resistors produces a conti

Designing an Experiment to Measure Current in a Complex Circuit

Propose an experimental procedure to measure the current distribution in a complex circuit containin

Determining Resistivity from Measured Data

A student measures several parameters of a wire in order to calculate its resistivity.

Effect of Adding a Parallel Resistor in a Series Circuit

Consider a circuit consisting of a 9 V battery connected in series with a 12 Ω resistor. A 24 Ω resi

Effect of Wire Cross-Sectional Area on Resistance

Resistance in a wire is given by the formula $$R = \rho \frac{l}{A}$$, where A is the cross-sectiona

Effects of Altering Capacitance on a Charged Capacitor

A capacitor with an initial capacitance of $$10\,\mu F$$ is charged to $$12\,V$$ by a battery, and t

Equivalent Resistance in Complex Resistor Networks

A circuit consists of five resistors arranged as follows: Resistors $$R_1$$ and $$R_2$$ (each $$10\,

Evaluating Conductance and its Relationship to Resistance

Electrical conductance, the reciprocal of resistance, is an important parameter in circuit analysis.

Experimental Design: Effect of Resistor Arrangements on Circuit Behavior

Design an experiment to investigate how different resistor configurations (series vs. parallel) affe

Experimental Errors in Electric Circuit Measurements

In a laboratory setting, students measure various parameters such as voltage, current, and resistanc

Graph Analysis: Charging Behavior in an RC Circuit

A graph is provided showing the voltage across a capacitor as a function of time while it charges in

Impact of Wire Dimensions on Resistance

In an experiment, two wires made of the same material but with different lengths and cross-sectional

Investigating Battery Life: Internal Resistance and Power Loss

A researcher is studying how the increasing internal resistance of a battery affects its performance

Investigating Capacitance: The Role of Plate Area and Separation

The capacitance of a parallel-plate capacitor is given by $$C = k*\epsilon_0*\frac{A}{d}$$, where $$

Investigating Temperature Dependence of Resistance

Resistance in metallic conductors generally increases with temperature. Answer the following:

Investigation of Non-Ohmic Behavior

A filament lamp exhibits non-ohmic behavior. The following graph shows its voltage versus current re

Measuring Electric Current and Voltage in a Simple Circuit

In a simple circuit consisting of a battery, a resistor, and connecting wires, you are asked to inve

Multi-Loop Circuit Analysis using Kirchhoff's Laws

Consider a circuit where a 15 V battery is connected in series with resistor $$R_1 = 50\,Ω$$. The ci

Ohm's Law and Circuit Analysis

A circuit consists of an ideal battery with an EMF of 12 V and a resistor of 6 Ω. First, assume the

Ohm's Law Application to Resistivity Measurement

A uniform wire of length 2 m and cross-sectional area $$1 \times 10^{-6} m^2$$ has a measured resist

Power Dissipation Analysis in Resistive Networks

Consider a circuit powered by a $$24 \text{ V}$$ battery. The circuit consists of a series resistor

RC Circuit Response to Voltage Change

Consider an RC circuit consisting of a resistor of $$100\,\Omega$$ and a capacitor of $$100\,\mu F$$

RC Circuit Transients and Time Constants

An RC circuit is comprised of a resistor $$R = 5\times10^3\,\Omega$$ and a capacitor $$C = 2\,\mu F$

Resistivity and Material Properties

In a study of different conductive materials, wires of identical dimensions (length = 2 m, cross-sec

Resistivity and Material Properties Experiment

A student investigates the influence of material properties on resistance by measuring wires made of

Role of Resistivity in Material Conduction

The resistance of a wire is given by the equation $$R = \rho \frac{l}{A}$$. A table below provides p

Series Circuit Analysis and Ohm's Law Application

A battery of 9 V is connected in series with two resistors: one having a resistance of 100 Ω and the

AC Generator Induced EMF Analysis

Consider an alternating current generator where a coil of $$N$$ turns and area $$A$$ rotates in a un

Analysis of Magnetic Torque on a Current Loop

A rectangular loop carrying a current $$I = 2.0$$ A is placed in a uniform magnetic field of strengt

Angle-Dependent Magnetic Force

A charged particle with $$q = +3 \times 10^{-6} C$$ is moving at a speed of $$v = 1 \times 10^5 m/s$

Calculating Magnetic Force on a Moving Charge

A charged particle moves through a uniform magnetic field. Use the information provided to answer th

Combined Effects of Motion and Rotation in a Varying Magnetic Field

A loop of wire is simultaneously moving linearly and rotating while situated in a time-varying magne

Comparing Magnetic Field Mapping Techniques

Design an experiment to compare two techniques for mapping magnetic field lines: one using iron fili

Comparing Magnetic Forces on Charges and Wires

This FRQ compares the magnetic force on an individual moving charge to the force on a current-carryi

Energy Transformation in a Moving Conductor Experiment

In an experiment, a conducting bar is made to slide through a uniform magnetic field, generating an

Evaluating Magnetic Flux Change in a Rotating Loop

A circular loop of wire is rotated in a uniform magnetic field. The change in orientation causes the

Experimental Verification of the Right-Hand Rule

Design an experiment to verify the right-hand rule by measuring the direction of the magnetic force

Force Comparison: Permanent vs. Electromagnets

In a laboratory experiment, the attractive force between a fixed magnet and a piece of iron is measu

Force on a Current-Carrying Wire in a Magnetic Field

A straight wire carrying an electric current is placed in a uniform magnetic field. Answer the follo

Force on a Moving Charge in a Magnetic Field

A charged particle moves through a uniform magnetic field. Analyze the factors affecting the magnitu

Force on Wire and Its Dependence on Current

An experiment measures the magnetic force on a current-carrying wire in a fixed magnetic field for d

Impact of Magnetic Field Orientation on Faraday Induction

A square loop with area $$A = 0.1$$ m² rotates in a uniform magnetic field of $$B = 0.5$$ T. Answer

Investigating the Effect of Coil Turns on Induced EMF

An experiment is conducted using solenoids with different numbers of turns to study their effect on

Magnetic Field Visualization

This FRQ explores the nature of magnetic fields and how magnetic field lines are used to represent t

Magnetic Field vs. Distance from Wire

A long, straight wire carrying a constant current produces a magnetic field whose strength decreases

Magnetic Force on a Moving Charge

A researcher examines the force on a charged particle moving in a uniform magnetic field. The partic

Magnetic Interaction between Bar Magnets

Two bar magnets are positioned with their poles aligned along a common axis, with the ability to adj

Mapping Magnetic Field Lines

A researcher is investigating the spatial distribution and behavior of magnetic fields around a perm

Measuring Deflections of Compass Needles in a Non-Uniform Magnetic Field

In this experiment, compass needles are placed at various distances from a bar magnet to record the

Motion of a Charge in Perpendicular Electric and Magnetic Fields

A charged particle with charge $$q$$ and mass $$m$$ enters a region where there is a uniform magneti

Motional EMF and Energy Conversion Analysis

A conducting rod of length $$l = 0.8 \; m$$ moves to the right at a constant speed of $$v = 4 \; m/s

Motional EMF and Velocity

In an experiment, a conducting rod moves perpendicular to a uniform magnetic field at various speeds

Net Force on a Current-Carrying U-shaped Wire

Consider a U-shaped wire immersed in a uniform magnetic field of magnitude $$B = 0.2 \; T$$ directed

Optimizing Solenoid Configuration for Maximum Magnetic Field

An engineer is tasked with designing a solenoid to produce the strongest possible uniform magnetic f

Rotating Coil and Faraday's Law

A circular coil rotates at a constant angular speed within a uniform magnetic field. During rotation

Testing Lenz's Law with a Falling Magnet Through a Coil

An experiment involves dropping a magnet through a coil and measuring the induced current. The claim

Time-Dependent Induced EMF in a Rotating Loop

Design an experiment to investigate how the induced emf in a rotating loop varies over time, particu

Torque on a Current Loop in a Magnetic Field

A rectangular current loop placed in a uniform magnetic field experiences a torque that tends to ali

Uniform Magnetic Field Inside a Solenoid

A solenoid is constructed with 400 turns and has a length of 0.25 m. It carries a current of 2 A. An

Converging Lens Experiment: Measuring Focal Length Using Object-Image Distances

Design an experiment to measure the focal length of a converging lens using object and image distanc

Convex Mirror Image Formation

This question examines the properties of images formed by convex mirrors and requires you to perform

Determining Lens Power: Experimental Measurement via Object-Image Distance

Design an experiment to determine the power of a converging lens by measuring object and image dista

Diffraction Grating for Wavelength Determination

A diffraction grating with 5000 lines per cm is used to measure the wavelength of a light source. Th

Diverging Lens: Sign Convention Error Analysis

In an experiment using a diverging lens, a student measures object distance, image distance, and ima

Electromagnetic Spectrum Frequency Comparison

Electromagnetic waves cover a wide range of wavelengths. Consider the following: a radio wave with a

Electromagnetic Waves: Frequency and Polarization

An electromagnetic wave in a vacuum travels at a constant speed of $$c = 3.0 * 10^8$$ m/s. Consider

Experimental Design: Evaluating Light Behavior in Combined Mirror-Lens Systems

An optical system combines a concave mirror and a converging lens to form an image. The following ta

Experimental Evaluation of the Electromagnetic Spectrum

Researchers often use a variety of techniques to measure the properties of electromagnetic radiation

Image Formation in a Compound Mirror System

A student investigates image formation using a compound mirror system consisting of a concave mirror

Image Formation with a Convex Mirror

An object 8 cm tall is placed 30 cm in front of a convex mirror with a focal length of -15 cm (using

Interference and Phase Difference in Wave Superposition

Consider two coherent light waves with a constant phase difference.

Investigating Snell's Law: Relationship between Incident and Refraction Angles

Design an experiment to study the relationship between the angle of incidence and the angle of refra

Optical Fiber Signal Loss Analysis

An optical fiber experiences a signal loss of 0.2 dB per meter. (a) Express the transmitted intens

Oscillating Charges and the Generation of EM Waves

An oscillating charge is a fundamental source of electromagnetic radiation. This problem involves ex

Plane Mirror Image Characteristics

This question explores the properties of images formed by plane mirrors and asks you to explain why

Polarization Effects in Electromagnetic Waves: Experiment Design

Design an experiment to investigate the effect of polarizing filters on the intensity of light. Your

Radiation Pressure and Electromagnetic Waves

An experiment measures the force exerted on a surface by electromagnetic radiation at various light

Single Slit Diffraction Analysis

A single slit with width $$a = 0.20 \text{ mm}$$ is illuminated by monochromatic light of wavelength

Single Slit Diffraction Analysis

In this question, you will derive the condition for minima in a single slit diffraction pattern and

Spherical Mirrors: Concave Mirror Analysis

An object of height 4 cm is placed 30 cm in front of a concave mirror with a focal length of 10 cm.

Thin Converging Lens Imaging

A bi-convex (converging) lens with a focal length of 10 cm is used to form an image of an object tha

Thin Diverging Lens Imaging

A diverging lens with a focal length of -15 cm is used to form an image of an object 9 cm tall place

Thin Film Interference and Optical Coatings

A thin film coating on a glass surface is designed to produce constructive interference for light of

Total Internal Reflection at Air-Water Interface

Light traveling within water (with an index of refraction $$n_{water} \approx 1.33$$) approaches the

Total Internal Reflection in Optical Fibers

An optical fiber has a core with an index of refraction of 1.50 and a cladding with an index of 1.40

Total Internal Reflection in Prisms

A triangular prism made of glass with an index of 1.6 is used to redirect a light beam. A light ray

Alpha Decay Analysis

A sample of a radioactive nuclide Y undergoes alpha decay according to the reaction: $$^{A}_{Z}Y \ri

Investigating Electronic Transition Spectra

A researcher examines the emission spectrum generated by electrons in a hydrogen-like atom with ener

Nuclear Composition and Isotope Identification

A researcher is examining a nuclide represented by $$^{63}_{29}X$$. Using this information, address

Photodisintegration of a Deuteron

A study is conducted on the photodisintegration of deuterium. Given that the binding energy of a deu