Physics Materials Revision for the Final Exam - 2025 Term II Notes

Capacitors

A capacitor is a device used to store electric charge.
Capacitors are used in many everyday applications (e.g., heart defibrillators, touch screens, camera flash units).
Capacitance is defined as the amount of charge stored per volt.
- Its unit is the Farad (F).
$C = \frac{Q}{V}$
For a parallel plate capacitor with a dielectric between its plates, the capacitance is given by:
- $C = \kappa \epsilon \frac{A}{d}$
  - Where:
    - $\kappa$ is the dielectric constant of the material.
    - $\epsilon$ is the permittivity of free space.
    - $A$ is the area of the plates.
    - $d$ is the distance between the plates.
  - If there is no dielectric (i.e., air between the plates), $\kappa = 1$ .
Total capacitance in series:
- $\frac{1}{C{equivalent}} = \frac{1}{C1} + \frac{1}{C2} + \frac{1}{C3} + …$
Total capacitance in parallel:
- $C{equivalent} = C1 + C2 + C3 + …$
If a circuit contains a combination of capacitors in series and parallel, identify the series and parallel parts, compute their capacitances, and then find the total capacitance.
Energy Stored in a Capacitor:
- The energy stored in a capacitor can be expressed in three ways:
  - $U_{stored} = \frac{1}{2}QV = \frac{1}{2}CV^2 = \frac{1}{2}\frac{Q^2}{C}$

Electric Current

Electric current is defined as the rate at which charge flows.
- $I = \frac{\Delta Q}{\Delta t}$ (Ampere)

Ohm's Law

$I \propto V$ (The current $I$ is directly proportional to the voltage $V$ ).
$I \propto \frac{1}{R}$ (The current $I$ is inversely proportional to the resistance $R$ ).
Therefore, $I = \frac{V}{R}$
- Units: $\frac{Volts}{Ohms} = Amperes$

Resistance

$R \propto L$ (The resistance is proportional to the length $L$ of a resistor).
$R \propto \rho$ (The resistance depends on the material of which the object is composed. $\rho$ is the resistivity of a substance).
$R \propto \frac{1}{A}$ (The resistance is inversely proportional to the cross-sectional area $A$ ).
Therefore, $R = \rho \frac{L}{A}$

Power

Power is the rate at which energy is dissipated.
- $P = \frac{E}{t}$ (Watt)
- $P = IV = \frac{V^2}{R} = I^2R$

Simple Circuits

A simple circuit is an electric circuit with only one power supply.
For a circuit in series:
- $Ib = i1 = i_2$
- $Vb = V1 + V_2$
For a circuit in parallel:
- $Ib = i1 + i_2$
- $Vb = V1 = V_2$

Resistors

Resistors in Series:
- $R{equivalent} = R1 + R_2 + …$
Resistors in Parallel:
- $\frac{1}{R{equivalent}} = \frac{1}{R1} + \frac{1}{R_2} + …$

Complex Circuits

Kirchhoff's Rules:
- Kirchhoff's Junction Rule.
- Kirchhoff's Loop Rule: $\sum V = 0$

Magnetic Forces

Magnetic force on a charge moving in a uniform magnetic field:
- $F = qv \times B = qvB \sin{\alpha}$
- Right-hand rule for the direction of magnetic force on a charge moving in a uniform magnetic field.
Radius of circular motion of the charge in a uniform magnetic field:
- $R = \frac{mv}{qB}$
Magnetic force on a current-carrying wire in a uniform magnetic field:
- $F = ILB \sin{\alpha}$
- Right-hand rule to determine the direction of the magnetic force on the wire.

Practice Problems

MCQ questions

MCQ Questions and Answers

A parallel-plate capacitor has plates of area A separated by distance d. If the distance between the plates is doubled while keeping the area the same, the new capacitance will be:
- B) $\frac{C}{2}$
A capacitor of capacitance C is charged to a potential difference V. The energy stored in the capacitor is given by:
- C) $\frac{1}{2}CV^2$
Three capacitors, each of capacitance C, are connected in series. The equivalent capacitance of the combination is:
- B) $\frac{C}{3}$
Two capacitors (C1 = 2uF) and (C2 = 4uF), are connected in parallel across a 12V battery. The total charge stored is:
- C) $72 \mu C$
Three capacitors (C1 = 2uF), (C2 = 3uF), (C3 = 5uF) are connected in parallel. Their equivalent capacitance is:
- B) $10 uF$
Two capacitors (C1 = 4uF), (C2 = 6uF) are connected in parallel to a 12V battery. The voltage across each capacitor is:
- C) Both (12V)
A (3uF) capacitor and a (6uF) capacitor are connected in parallel to a 9V battery. The ratio of charges (Q1 : Q2) stored on them is:
- B) (1:2)
Two identical capacitors (C = 5uF) are connected in parallel to a 10V battery. The total energy stored is:
- B) $500 uJ$
If an additional capacitor is connected in parallel to an existing parallel combination, the total capacitance:
- C) Increases
Electric current is defined as the:
- A) Flow of electric charge per unit time
According to Ohm's Law, the current (I) through a conductor is:
- C) Directly proportional to voltage (V)
The resistance of a wire depends on:
- A) Length (L) and resistivity ($\rho$)
Current density (J) in a conductor is given by:
- B) $\frac{I}{A}$
If the voltage across a resistor is doubled while keeping its resistance constant, the current through it:
- B) Doubles
The resistivity ($\rho$) of a material depends on:
- B) Temperature and material type
Three resistors (R1= 2$\Omega$), (R2 = 3$\Omega$), (R3 = 5$\Omega$) are connected in series. The equivalent resistance is:
- B) 10$\Omega$
At a junction in a circuit, three currents meet: (I1 = 2A) entering, (I2 = 1.5A) leaving. What is I3 = ?
- B) 0.5 A leaving
A (6$\Omega$) resistor and a (4$\Omega$) resistor are connected in parallel to a 10 V battery. What is the total power dissipated?
- B) 25 W
ohm is denoted by a symbol
- 1. $\Omega$
The resistivity does not change if
- 3.The shape of the resistor is changed
the poorest in electrical conductivity a mong the following material is
- 3. aluminium
A device used to measure a current in electric circuit is?
- A. Ammeter
Three identical resistors are connected in parallel . Which statement is right for this connection?
- B. They have different current but the same potential difference
The wire above has a current being carried to the right and point P is a distance r from the wire. What is the direction of the magnetic field at P?
- B. Into the page
A current carrying wire of length L and mass m is placed in a uniform magnetic field B. The current in the wire is I. What must the direction of the field be in order to balance the gravity?
- A. Out of the page
An electron enters a region of uniform magnetic field in the -Z direction. What is the direction of the magnetic force on the electron due to the magnetic field?
- B. +Y direction
In which direction will the electric force from the two equal positive charges move the negative charge shown below?
- A. North
Two charges separated by a distance d, if one of the charges doubles, and the distance between them is reduced to its half, what happens to the coulomb’s force between these two charges?
- B. F = 8 Fo
A proton is released from rest in a uniform electric field and accelerates to the east at a rate of 3 x 107 m/s2. What is the magnitude of the electric field E? (knowing that F = ma)
- B. 1.872 N/C
A uniform wire of resistance 100 $\Omega$ is cut into 5 parts of equal length and cross-sectional area. These parts are now connected in parallel. The equivalent resistance of the combination is:
- B. 4 $\Omega$
In the given figure, the voltage across R is:
- D. 17 V

Short and Long Questions

When five capacitors with equal capacitances are connected in series, the equivalent capacitance of the combination is 6.00 mF. The capacitors are then reconnected so that a parallel combination of two capacitors is connected in series with a parallel combination of three capacitors. Determine the equivalent capacitance of this combination in millifarads
Calculate the magnitude of the charge stored on each plate on the capacitor in the circuit shown in the figure below.
Three 0.18-μF capacitors are connected in parallel across a 12-V battery, as shown in the figure above. The battery is then disconnected. Next, one capacitor is carefully disconnected so that it doesn’t lose any charge and is reconnected with its positively charged and negatively charged sides reversed.
- A. What is the potential difference across the capacitors now?
- B. What is the stored energy of the combination of capacitors after they have been rearranged?
- C. Then the space between the plates of one of the capacitors is completely filled with a conducting material without changing the arrangement. What happens to the energy stored in the combination of capacitors after the conducting material is added?
Lightning bolts can carry as much as 30 C of charge and can travel between a cloud and the ground in around 100 ms. Potential differences have been measured as high as 400 million V. Calculate the average current in such a lightning strike. Calculate the resistance of the air during such a lightning strike. Calculate the total energy delivered during such a strike. Approximately 100 strikes from cloud to ground occur on Earth every second. Suppose each lightning strike is as described in the introduction to this problem and calculate the maximum power transferred to Earth by lightning. Electric energy end use in the United States in the year 2017 was approximately 1.38 billion kWh. Calculate the number of minutes required per year for lightning strikes with maximum power to deliver the equivalent of the 2017 U.S. electric energy end use.
Two resistors, A and B, are connected in series to a 6.0-V battery; the potential difference across resistor A is 4.0 V. When A and B are connected in parallel across a 6.0-V battery, the current through B is 2.0 A. The battery has negligible internal resistance. Calculate the resistances of A and B.
A metal wire of resistance 48 $\Omega$ is cut into four equal pieces that are then connected side by side to form a new wire, which is one-quarter of the original length. Calculate the resistance of the new wire.
The four resistors shown in the figure have an equivalent resistance of 8 $\Omega$ . Calculate the value of Rx.
How much power is dissipated in each resistor shown in the figure?
A wire of length 2 m and cross sectional area 0.05 m2 and resistance 20 $\Omega$ . What is the Resistivity of the wire?
Two conductors are made of the same material and have the same length L. Conductor A is a hollow tube with inside diameter 2.00 mm and outside diameter 3.00 mm; conductor B is a solid wire with radius RB. What value of RB is required for the two conductors to have the same resistance measured between their ends?
Suppose the voltage output of the battery is 12.0V, and the resistors 1=1.00 $\Omega$ , 2=6.00 $\Omega$ , and 3 = 13.0 $\Omega$ are in series.
- a- What is the total resistance?
- b- Find the current across the battery
- c- Calculate the voltage drop in each resistor, and show these add to equal the voltage output of the source.
- d- Calculate the power dissipated by each resistor.
- e- Find the power output of the source, and show that it equals the total power dissipated by the resistors.
Let the voltage output of the battery and resistances in the parallel connection: =12.0V, 1=1.00 $\Omega$ , 2=6.00 $\Omega$ , and 3=13.0 $\Omega$ .
- a- What is the total resistance?
- b- Find the total current.
- c- Calculate the currents in each resistor, and show these add to equal the total current output of the source.
- d- Calculate the power dissipated by each resistor.
- e- Find the power output of the source, and show that it equals the total power dissipated by the resistors.
What is the current in the circuit shown in the figure when the switch is (a) open and (b) closed?
For the circuit shown in the figure below , R1 = 6.00 $\Omega$ , R2 = 6.00 $\Omega$ , R3 = 2.00 $\Omega$ , R4 = 4.00 $\Omega$ , R5 = 3.00 $\Omega$ , and the potential difference is 12.0 V.
- a) What is the equivalent resistance for the circuit?
- b) What is the current R1 through R5? V
- c) What is the potential drop across R3?

ELECTRIC CURRENT - CIRCUITS WORKSHEET

the equivalent (total) resistance for each of the following circuits below.
In a series circuits below In circuit A there is just one path so the charge flow is constant everywhere (charge is not lost or gained). In circuit B. adding 2 more identical resistances of the same original resistor in series to the circuit .
- a) How is the charge flow out of the battery (and back into it) affected by adding more bulbs in series?
- b) If the resistors were light bulbs, how do you expect the brightness of the bulbs to be by adding more bulbs in series?
- c) How is the brightness in the 2 circuits related to charge flow or current?
- d) How does the current in circuit B compare to circuit A?
- e) How is current (I) related to the resistance of the circuit?
- f) If the resistance of a circuit A is quadrupled, by what factor does the current change?
- g) Complete the table below regarding to information given .
- h) Is there a relationship between resistance and voltage drop in a series circuit? If so, state it.
- i) If the resistors were light bulbs, explain in terms of charge flow (current) and energy per charge (voltage) which bulb would be brightest / dimmest.

Circuit position	Voltage (V)	Current (A)	Resistance ($\Omega$)	Power (W)
1	10
2	20
3	30
Total	6

Repeat problem 2, and fill in the table, considering now R1, R2, and R3 connected in parallel.
8) A 6.0-ohm lamp requires 0.25 ampere of current to operate. In which circuit below would the lamp operate correctly when switch S is closed?
A 110-V household circuit that contains an 1800-W microwave, a 1000-W toaster, and an 800-W coffeemaker is connected to a 20-A fuse. Determine the current. Will the fuse melt if the microwave and the coffeemaker are both on?

Circuit position	Voltage (V)	Current (A)	Resistance ($\Omega$)	Power (W)
1	10
2	20
3	30
Total	6

21.

R ($\Omega$)	$\Delta$ V (V)	I (A)	P (W)
Battery	3
3		3
24			8
10	15
		6	5

In the circuit shown in the figure, V1 = 1.5 V, V2 = 2.5 V, R1 = 4 $\Omega$ , R2 = 5 $\Omega$ . What is the magnitude of the current i1, flowing through resistor R1?
The circuit shown in the figure consists of two batteries supplying voltages VA and VB and three light bulbs with resistances R1, R2, and R3. Calculate the magnitudes of the currents i1, i2, and i3 flowing through the bulbs. Indicate the correct directions of current flow on the diagram. Calculate the power, PA and PB, supplied by battery A and by battery B.
Problem 1:
- A) Solve for I1, I2, and I3
- B) Find Req, then fine I1 using ohm’s law

Problem 2:

a) Find a relation between the three currents.
b) Now using kirchhoff’s loop rule solve for I1, I2, and I3

Problem 3:

Solve for I1, I2, and I3

Problem 4:

Solve for V1, V2, and R4

Magnetism: Forces and Fields

A particle of charge +q enters a uniform magnetic field B directed into the page. The direction of the magnetic force FB on the particle is:
- (A) top of the page
A particle of charge -q enters a uniform magnetic field B directed out of the page. The direction of the magnetic force FB on the particle is:
- (B) bottom of the page
A particle of charge -q enters a uniform magnetic field B to the right. The direction of the magnetic force FB on the particle is:
- (A) top of the page
A charged particle, –q, enters a uniform magnetic field B. If FB is the magnetic force, which of the following represents the particle’s velocity?
- (C) FB/qB
A current carrying wire carries a current into the page. The wire is placed in a uniform magnetic field directed to the right. The magnetic force on the current is directed:
- (B) bottom of the page
A current carrying wire of length L and mass m is placed in a uniform magnetic field B. The current in the wire is I. What must the direction of the field be in order to balance the gravitational force?
- (E) out of the page
A current carrying wire of length L and mass m is placed in a uniform magnetic field. The current in the wire is I. What must the magnitude of the field be in order to balance the gravitational force?
- (A) $\frac{mg}{IL}$
A positive charge travels through a uniform magnetic field. The diagram represents the direction of the particle’s velocity and magnetic force on it at the certain point. What is the direction of the magnetic field B?
- (B) into the page
An electron experiences a magnetic force 4.8x10-13 N when entering a uniform magnetic field of strength of 2 T at a 30°angle to the magnetic field lines. Which of the following represents the electron’s speed?
- (C) 3x10^6 m/s
A negatively charged particle of charge q and mass m moves with constant speed v in a circular path in the presence of a uniform field B. Which of following represents the radius r of the moving charge?
- (E) $\frac{mv}{qB}$
An electron enters a region where both a magnetic field B into the page and electric field E between the two plates act on the particle as shown above. What must be the direction of the electric field in order for the particle to move in the straight line?
- (B) bottom of the page
An electron enters a region where both a magnetic field B into the page and electric field E between the two plates act on the particle as shown above. Which of the following represents the particle’s velocity when it passes through the region of two fields undeflected?
- (A) E/B
An electron enters a region where both a magnetic field B into the page and electric field E between the two plates act on the particle as shown above. If the electric field is removed, which of the following represents the motion of the electron?
- (D) Circular path clockwise
An electric current flows in a closed loop made of two fixed rails, power supply, and a very light rod that is free to move on the top of the rails. A uniform magnetic field is perpendicular to the plane of the circuit. What is the direction of the magnetic force on the rod?
- (D) +x
An electric current flows in a closed loop of resistance R made of two fixed rails, a battery supplying V, and a very light rod of length L that is free to move on the top of the rails. A uniform magnetic field B is perpendicular to the plane of the circuit. What is the magnitude of the magnetic force on the rod?
- (A) $\frac{VBL}{R}$
A rectangular piece of metal is placed in a uniform magnetic field and connected to a battery on two opposite sides. Which one of the following statements is incorrect?
- (D)Point N has higher potential that point L.