AP Physics Full Review Notes

AP Physics Full Review: Past Exam Breakdown

1. Energy (25%)

2. Dynamics/Newton's Law (20%)

3. Kinematics (17%)

4. Rotational Motion (16%)

5. Momentum (14%)

6. Circular Motion/Gravitation (5%)

7. Simple Harmonic Motion (3%)

Kinematic Equations & Motion Graphs

• Position Graph: Velocity is the slope.
• Velocity Graph: Acceleration is the slope; Area under the curve is displacement.
• Acceleration Graph: Area under the line is velocity.

Basic Formulas

• Acceleration: $a = \frac{\Delta v}{\Delta t}$
• Velocity: $v = \frac{d}{t}$
• Average Velocity: $V<em>{avg} = \frac{V</em>1 + V_2}{2}$

Projectile Motion

• Horizontal Motion: Velocity, displacement, time.
• Vertical Motion: Initial velocity, final velocity, displacement, time, acceleration.
• Horizontal time = vertical time.
• Apply kinematic equations to find vertical quantities and then use those to find horizontal quantities.
• At the highest point, $t = \frac{-V_{oy}}{-g}$
• With an angle:
  • Break down by horizontal and vertical components.
  • Use kinematics.
  • Apply the average velocity equation to find missing horizontal quantities $(v = d/t)$.
• If up to the right, sine is for vertical and cosine for horizontal.
• Horizontal range: $\frac{V_{oy}^2 \times sin2(\theta)}{g}$

Forces & Newton’s Laws

1. A center of mass at rest will remain at rest unless acted upon by a net force; a moving center of mass will maintain a constant velocity unless acted upon by a net force.
2. The acceleration of an object/system is equal to the net force acting upon it divided by its mass: $a = \frac{f_{net}}{m}$
3. Every action has an equal and opposite reaction; action-reaction requires 2 forces from 2 objects acting on each other.

Equilibrium

• Static Equilibrium: Net force on a MOTIONLESS object/system is 0.
• Dynamic Equilibrium: Net force on a MOVING object/system is 0 (constant velocity, no acceleration).
• If it’s not moving or at a constant rate, all forces are balanced.

Normal Force & Friction

• Normal force acts perpendicular to the surface applying it: $F_g = mg$
• Friction force acts parallel to the surface applying it (static stops it from moving, kinetic slows it).
  • Static Friction (Fs): Acts on motionless object; magnitude/direction will always be whatever keeps the object from moving $(F<em>s < M</em>s \times F_n)$; static friction will oppose the applied force until it reaches the max (then kinetic).
  • Kinetic Friction (Fk): Acts on moving objects once the static friction threshold has been passed; direction is always opposite the direction the object is moving $(F<em>k = M</em>k \times F_n)$, where M is the coefficient of friction.
  • Sine makes it slide, cosine keeps it close (cos into the ramp, sine down it).

Atwood Machines

• Two masses hanging from a massless string with a massless/frictionless pulley.
• Tension is consistent in the string and accelerations are always equal.
• Considered a system, gravity is all that will accelerate it.
• $F<em>{net} = ma = T</em>g - T = ma - T$ which means $T = mg - ma$
• If $m<em>1 + m</em>2$, the system is in equilibrium (dynamic or static) but if not, it accelerates.
• Newton’s third law: $a = \frac{F_{net}}{m}$
• The downwards force of one block minus the net force would give you the force of tension.
• If an object is sliding or traveled a distance down (like on a ramp), the velocity at the bottom can be found with $v = \sqrt{2gh}$
• If going down a frictionless ramp, $M_k = \frac{h}{x}$

Mechanical Energy

Work

• Work (w) is the mechanical transfer of energy to or from an object/system by pushing or pulling; occurs when a force is applied and displaces an object/system.
• Scalar quantity.
• Formula: $W = Fdcos(\theta)$ or $KE<em>f - KE</em>i$
• Positive work: Adds mechanical energy to the system; occurs when a component of the applied force and displacement are in the same direction ($\Theta$ is between 0 and 89).
• Negative work: Takes mechanical energy from the system; occurs when the applied force and displacement aren’t in the same direction ($\Theta$ is between 91 and 180).
• Work that is perpendicular to the direction of intended motion does zero work.
• Work is the area under a force by position graph.

Energy

• Kinetic Energy: The energy of motion, measured in Joules (J); changes in kinetic energy require work! $K = \frac{1}{2}mv^2$ (if KE is doubled, velocity increases by a factor of $\sqrt{2}$).
• Potential Energy: Energy an object COULD have if released into motion, measured in Joules (J).
  • Gravitational Potential Energy (Ug): Energy attributed to an object/system based on its location in a gravitational field $(U_g = mgh)$; if no friction, $\frac{1}{2}v^2 = gh$ because mass cancels out.
  • Elastic Potential Energy (Us): Energy attributed to an object/system based on its contact with a stretched or compressed spring $(U_s = \frac{1}{2}kx^2)$
• Conservation of Energy: The total energy of an isolated system will be constant; mechanical energy will always be conserved in the absence of friction; work is always required to increase or decrease total mechanical energy.
• Blocks on ramps: Steeper = faster; the height says they’ll have the same velocity at the end (steepness affects time, height affects final velocity and $\Delta x$ if becoming a projectile).
• $M<em>k = \frac{F</em>f}{F_n}$

Power

• Power (P) is the rate at which energy changes state.
• Scalar quantity measured in watts (W), 1 W = 1 J/s.
• Multiply watts by time to get joules if constant rate.
• $P = F \times v$ or $P = \frac{W}{t}$, so $P = \frac{Fd}{t}$ or $P = Fvcos\Theta$

Momentum & Impulse

• Momentum is the tendency to remain in motion, always conserved.
• Impulse (J) is the change in momentum.
• Impulse is the area under a force by time graph.
• $I = f\Delta t$ or $I = \Delta(mv)$
• So it follows that $f \times t = m \times change \space in \space v$

Elastic Collisions

• Elastic collisions conserve the momentum and kinetic energy of the system.
• They bounce off each other.
• Law of Conservation of Momentum: The total momentum of an isolated system is constant because it’s unchanged by inner events.
• For elastic collisions, $P<em>{1i} + P</em>{2i} = P<em>{1f} + P</em>{2f}$

Inelastic Collisions

• They conserve momentum (p in a system is always conserved) but do not conserve kinetic energy.
• Objects begin separately, collide, and frequently stick together if perfectly inelastic.

Explosions

• They conserve momentum but not kinetic energy.
• They start as 1 object and explode into 2.

Center of Mass

• The center of mass is essentially where something would balance on a fulcrum.
• It can be calculated by establishing a point (where x=0) then multiplying each massive part’s distance from that times it’s mass. Add those values together and divide by the total mass.

Closed vs Open Systems

• If energy is changed by something outside of the objects in question, it is open.
• Closed systems conserve energy.
• If losing energy to the surroundings (taking from the objects that classify system) it means it’s open.
• Friction means it’s open / mechanical energy is conserved in the absence of friction.

Circular Motion & Gravitation

The Basics

• Uniform circular motion is the motion of an object moving along a circular path at a constant speed.
• Tangential speed is constant.
• Tangential velocity is not constant (+ and -).
• Tangential velocity is always TANGENT to the circular path.

Centripetal Acceleration & Force

• Centripetal acceleration is directed towards the center of a circular path that turns an object but does NOT change its speed. It is measured in $m/s^2$, and is a vector; can be solved with: $A_c = \frac{v^2}{r}$ (v being tangential velocity).
• Centripetal force is the force that produces the centripetal acceleration necessary to turn an object; the net force going into the middle of the circle (could be Fn, Fg, etc). It is perpendicular to motion so it can’t do work $(cos90 = 0)$. It is measured in Newtons and is a vector. Do not label on free body diagrams. Centripetal force is centripetal acceleration times mass or $F<em>c = m \times (\frac{v^2}{r})$ or $F</em>c = mw^2r$; if an object’s going in a circle on a rope, $F<em>t - F</em>g = F_c$.
• If a planet is in orbit, gravitational force is the centripetal force so $\frac{GMm}{R^2} = \frac{mv^2}{R}$

Gravity

• Newton’s Law of Universal Gravitation: The gravitational force exerted between 2 objects is directly proportional to the mass of each; it is also inversely proportional to the squared distance between the objects’ centers of mass! Or, and far more simply, $F<em>g = \frac{Gm</em>1m_2}{r^2}$ (if distance between particles is 2x, the force decreases by factor of 4).
  • $G = 6.67e^{-11}$ (gravity constant).
  • $F_g$ (the force of gravity) also refers to the strength of the field.
• Gravitational field (g): The invisible field that surrounds any mass and applies a force on any other object with mass.
  • Always directed toward center of mass.
  • Gravitational strength is directly related to the gravitational constant (by planet) and the mass of the source (the bigger the mass it’s coming from, the stronger).
  • Gravitational strength is inversely related to the squared distance from the source (the farther, the weaker).
  • Gravitational field strength: $g = \frac{GM}{r^2}$ (on earth that’s the 9.81 number I think).
• Gravitational potential energy: Find the GPE between 2 objects/systems using $U<em>g = \frac{Gm</em>1m_2}{r}$
• Earth’s radius: $6.37 \times 10^6$
• Earth’s mass: $5.973 \times 10^{24}$
• $G = 6.67e^{-11}$
• So, if it involves earth, $U<em>g = \frac{(6.671E^{-11})(5.973E^{24})(m</em>2)}{6.37E^6}$

Orbits

• For one orbit/revolution, $v = \frac{2\pi r}{T}$ and since $A<em>c = \frac{v^2}{r}$, then $A</em>c = \frac{4\pi^2r}{T^2}$
• Also $F<em>c = \frac{mv^2}{r}$ so for 1 revolution, $F</em>c = \frac{4 \pi^2mr}{T^2}$

Rotational Motion

Rotational Quantities

• Types of motion:
  • Translational motion: The whole object moves across a trajectory.
  • Angular motion: Rotation (every point moves along a circle).
  • Combination motion: Rotating while traveling a trajectory (has both rotational kinetic energy and kinetic energy).
• Angular Velocity (ω): The # of radians an object rotates in a certain time; every point on a rotating rigid body has the same angular velocity. $(w = \frac{angle \space of \space rotation}{time})$
  • Angular velocity is the area under an angular velocity by time graph.
• Angular Acceleration (α): The rate at which a rotating object’s angular velocity is changing with respect to time ($aa = \frac{change \space in \space angular \space velocity}{time}$ or $\frac{torque}{inertia}$).
  • Angular acceleration is the slope of an angular velocity by time graph.
  • AA is constant with constant torque.
• Translational quantities are the rotational analog times the radius.

Torque

• Torque is the rotational analog to force.
• Torque is required in order to change an object’s angular velocity.
• Torque is a vector that uses the Newton-meter unit.
• Solved with $T = Frsin(\theta)$ and $T = Iaa$ where r is the length of the lever and theta is the angle between the force and arm (max at 90 degrees).
  • The lever arm is the perpendicular distance from the axis of rotation/revolution to the line of the applied force.
  • Only the force component perpendicular to the lever arm can affect torque.
  • Negative torque goes clockwise and positive torque goes counter-clockwise.
  • Net torque is proportional to impulse.
  • Any force coming from the center of an object will not apply torque.
  • Net torque is the slope of angular momentum by time graph.
  • If torque is constant, so is angular acceleration.
  • If net torque is 0, net force is 0 and vice a versa.

Equilibrium

• Rotational equilibrium occurs when the net torque on an object is zero (like a balance).
• Static equilibrium is when an object is at rest, 0 net force and 0 net torque.
  1. Pick an axis/pivot that removes an unknown
  2. Determine the torque created by each force
  3. Determine the sign of each torque around the pivot point
  4. Write the equations for Fnet=0 and Tnet=0
  5. Solve the equations

Inertia

• Moment of inertia: A measure of how easily an object can rotate.
  • Rotation is dependent on mass distribution.
  • Standard unit is $kgm^2$
  • Inertia is the slope of a torque by angular acceleration graph.
• Newton’s 2nd Law for Rotation: An object that experiences a net torque about the axis of rotation undergoes an angular acceleration.
  • Solved with aa=Tnet/I (moment of inertia) so smaller inertia, greater aa.
• Inertia has a quadratic relationship with $r^2$ and a linear relationship with mass.
• When inertia increases, the angular velocity decreases.
• Inertia formulas:

Angular Momentum

• Angular momentum (L): The momentum attributed to the rotation of an object.
• A change in angular momentum requires a torque applied over a time interval.
• Angular momentum can be solved by multiplying inertia and angular velocity (L=IW) and the change can be determined by multiplying torque and time ($\Delta L = Tt$).
• Conservation of Angular Momentum: The angular momentum of a rotating object/system subject to no external torque is conserved.

Rotational Kinetic Energy

• RKE is the KE of a rotating object.
• The total KE is always more than a nonrotating object at the same speed.
• If an object is rotating AND has a linear displacement, part of its energy is KE and part is RKE. Thus, a rotating object will always take longer to travel down an incline when compared to a sliding one (the sliding one doesn’t have to split energy).
• RKE is solved with $K<em>{rot} = \frac{1}{2}Iw^2$ or $K</em>{rot} = \frac{1}{2}I(\frac{v}{r})^2$
• Rotating object on a trajectory: $U<em>g = K</em>{trans} + K<em>{rot}$ or $K</em>{total} = \frac{1}{2}mv^2 + \frac{1}{2}Iw^2$

Simple Harmonic Motion

The Basics

• Simple harmonic motion is an example of periodic motion where the restoring force is directly proportional to the distance stretched or compressed.
• Amplitude: The initial displacement (how far it’s pushed back).
• Period (T): Measured in s, the time required for a system to complete 1 revolution $(2\pi r)$.
• Frequency (f): Measured in Hertz (Hz), it’s the # of revolutions/cycles in a unit of time; $F = \frac{1}{T}$
• Handy dandy table!

Hooke’s Law

• Hooke’s Law states the restoring force is equal to the spring constant times the displacement from equilibrium, aka $F<em>s = kx$ (k is slope of $F</em>s$ by x graph).
• Equilibrium: The position where the spring/mass-spring system experiences 0 net force.
• Spring constant (k): Measured in N/m, it qualitatively means tightness and quantitatively means the amount of force needed to stretch it 1m.
• Restoring force: It pushes a stretched/compressed object towards equilibrium.
• Max speed at equilibrium where all energy is KE and min speed at amplitude when all energy is PE.
• Spring energy: $U_s = \frac{1}{2}kx^2$ or $PE = \frac{1}{2}kA^2$ (a is amp).

Periods

• Mass-spring systems: Systems consisting of a massive object that’s attached to one end of a spring; $T_s = 2\pi(\sqrt{\frac{m}{k}})$
• frequency would be $\frac{1}{2\pi} \times \sqrt{\frac{k}{m}}$
• Pendulum: A system of a massive object (the bob) suspended by a string/rod; $T_p = 2\pi(\sqrt{\frac{l}{g}})$, where l is the length of the pendulum and g is gravity’s a frequency would be $\frac{1}{2\pi} \times \sqrt{\frac{g}{l}}$
• Impacts of other variables:
  • Period is affected by m and k but not by x, the extra stretch is compensated for by extra energy
  • Double the spring constant (k), f goes up by root 2
  • Half the length (l), divides period (T) by root 2
  • If angular momentum (L) increases, period (T) increases (slower)

Waves

Transverse Waves

• Crests are points of maximum vertical displacement above the horizontal
• Troughs are points of maximum vertical displacement below the horizontal
• One wavelength is measured as the distance between 2 adjacent crests or troughs
• Amplitude is the maximum displacement from the horizontal to either a crest or trough

Period and Frequency

• The time it takes for one complete vertical oscillation is called the period (T)
• The number of cycles it completes in one second is called frequency (f)
• Period and frequency are inverses of each other
  • $T = \frac{1}{f}$ and $f = \frac{1}{T}$
• To find the speed of a wave:
  • distance = rate × time
  • wavelength = speed × period
  • $v = f \lambda$

Wave Speed on a Stretched String

• Speed of a transverse wave on a stretched spring: $v = \sqrt{\frac{F_T}{\mu}}$
  • Linear mass density ($\mu$) mass of string/length of string
  • FT is force due to tension

Big Wave Rules

• Rule #1: The speed of a wave is determined by the type of wave and the characteristics of the medium, not by the frequency
• Wave Rule #2: When a wave passes into another medium, its speed changes, but its frequency does not

Superposition of Waves

• When 2 or more waves meet and overlap (interfere), the displacement at any point of the medium is equal to the algebraic sum of the displacement due to the individual waves
• Constructive interference: occurs when 2 waves with both positive or negative displacement overlap and the combined wave has a displacement of a greater magnitude than either one of the individual waves
• Destructive interference: waves that have opposite displacements meet and the combined wave has a magnitude less than each of the individual waves
• In Phase: waves combine and crest meets crest, trough meets trough, then constructive interference occurs
• Out of Phase: waves combine and crest meets trough and trough meets crest, meaning that destructive interference is occurring

Standing Waves

• Combination of 2 waves moving in opposite directions. Also known as stationary waves
• Nodes and antinodes always alternate, are equally spaced, and the distance between the 2 is equal to $\frac{1}{2}$ a wavelength
• $L = n(\frac{1}{2}\lambda)$
  • L=length of string
  • Length of string must be a multiple of 12 λ to form a standing wave
  • n is an integer known as the harmonic number
• $\lambda_n = \frac{2L}{n}$
  • This is the equation for the wavelength of a standing wave
• Harmonic frequencies equation: $f_n = n\frac{v}{2L}$

Sound Waves

• Are produced by the vibration of an object which cause pressure variations in the medium of relevance
• Compressions: when molecules are closer together in a medium (high pressure)
• Rarefactions: when molecules are further apart (low pressure)
• Sound waves are longitudinal and move parallel to the direction of wave propagation
• Sound waves speed equation: $v = \sqrt{\frac{B}{\rho}}$
  • density = p
  • B = bulk modulus (medium that is easily compressed(gas) has a low bulk modulus while liquids and solids tend to have a higher bulk modulus)

Beats

• A beat has occurred each time a wave constructively interferes
• The number of beats/second is known as beat frequency
  • Equation for beat frequency: $f<em>{beat} = |f</em>1 − f_2|$
  • Unit: Hz

Resonance for Sound Waves

• Resonant wavelengths and frequencies for a closed tube: ${ \lambda<em>n = \frac{4L}{n} }$ and ${ f</em>n = \frac{nv}{4L} }$ for any odd integer n
• Resonant wavelengths and frequencies for an open tube: ${ \lambda<em>n = \frac{2L}{n} }$ and ${ f</em>n = \frac{nv}{2L} }$ for any integer n

The Doppler Effect

• Change in frequency of a wave in relation to a detector which is moving relative to the wave source
• If the detector is moving toward the source, higher frequencies are detected and waves are emitted at a higher rate
• If the source is moving toward the detector, then detector receives shorter wavelengths and higher frequencies

Electric Forces and Fields

Electric Charge

• Basic Components of Atoms: protons, neutrons, and electrons
• Electrons circle the nucleus which is made up of nucleons (protons and electrons)
• An atom is held together by the electromagnetic force, which helps in allowing the electrons to orbit the nucleus
• Electric charge allows protons (positively charged) and electrons (negatively charged) to attract
• Most atoms contain an equal number of protons and electrons which causes the electric charge to be 0 because the negative charges cancel out the positive charges
• Ionization must occur to charge matter (negatively or positively) because this creates an imbalance in the number of protons and electrons
  • Ex: Removing electrons = positive charge Adding electrons = negatively charged
• Charge is conserved and net charge (total amount of charge) cannot be created or destroyed
• Elementary charge (e) is the basic unit of electric charge and is the magnitude of charge on an electron/proton
• Charge of an ionized atom must be a who number (n) multiplied with e because charge can only be manipulated by variations of the quantity of e (n=1,2,3….)
• Charge is quantized, so the charge of a particle or object is denoted by q Equation: $q = n(\pm e)$

Coulomb’s Law

• Coulomb’s Law is defined by the equation: $F<em>E = k \frac{q</em>1q_2}{r^2}$
  • $F<em>E$ represents electric force. A negative $F</em>E$ is an attraction between charges and a positive $F_E$ is repulsion
  • $q<em>1$ and $q</em>2$ represent particle charges
  • r represents the distance between 2 charges
  • k is a constant. In a vacuum or air, it is known as Coulomb’s constant with a value of $k_0 = 9 \times 10^9 \frac{N \times m^2}{C^2}$ *force vectors point toward each other for attraction and away for repulsion
• Permittivity of free space is a constant denoted by $\epsilon_0$ which equals: $8.85 \times 10^{-12} \frac{C^2}{N \times m^2}$
  • $k_0$ is usually written in terms of this constant
  • $k<em>0$ in terms of $\epsilon</em>0$ is: $k<em>0 = \frac{1}{4\pi\epsilon</em>0}$
• $F<em>E = \frac{1}{4\pi\epsilon</em>0} \times \frac{q<em>1q</em>2}{r^2}$ would then be the equation for Coulomb’s Law for the force between 2 point charges

Superposition

• Net electric field produced at any point by a system of charges is equal to the vector sum of all individual fields, produced by each charge at this point
  • $E = E<em>1 + E</em>2 +…+ E<em>n = \sum E</em>i$
• n = total number of charges in the system units: Newtons (N)

The Electric Field

• Similarly to how a gravitational field created by Earth provides a gravitational force to any mass in the field, the presence of a charge creates an electric field in the space that surrounds it
• $E = \frac{F \space on \space q}{q}$
  • $F \space on \space q$ is the force the test charge experiences
  • q is the test charge
  • E the resulting electric field vector
• If the source charge is positive, field vectors point away (remember: positive=repulsion)
• If the source charge is negative, field vectors point towards it (remember: negative=attraction)
• Force and the electric field decrease as they get further away from the charge (indicated by smaller arrows/vectors)
• Field lines determine strength of field:
  • Dense: stronger field
  • Sparse: weaker field
• Electric field vectors can be added like any other vectors
  • Ex: If there were 2 source charges (+Q and -Q) their fields would combine: $E<em>{total} = E</em>1+E_2$ (form of superposition) If done in various positions in space, these two equal but opposite charges will form a pair called electric dipole
• The force generated on a charge that is an electric field is shows by the equation: $F = qE$ *When finding the acceleration of particles, work done on a particle during collisions, speed of particles, and time, use the big 5 kinematic equations along with the new ones to find your answers

Direct Current Circuits

Electric Current

• If electrons move randomly, there is no net movement, which means no current
• River, Current analogy: A current is like a river. In the river, water is moving at some rate and in a current, electric charge is moving at some rate
• Drift Speed (vd): average velocity of charged particles
• Current is measured by how much charge crosses a plane per unit time: $I_{avg} = \frac{\Delta Q}{\Delta t}$
  • charge/time = Coulomb’s/second = 1 ampere (A)
  • 1 C/s = 1 A
• The direction of the current is taken to be the direction that positive charge carriers would move o Ex: if electrons drift to the right, the current is moving towards the left

Resistance

• River, Resistance analogy: Resistance would be the part of the river that zigzags/increases length, providing resistance to the flow of water
• (Ohm’s Law) Resistance equation: $R = \frac{V}{I}$
  • I = current
  • V = voltage (potential difference)
  • Unit: volts/amp = 1 ohm (Ω, omega) = 1 Ω
  • Only works if resistor is already connected to other elements in circuit
• Alternative Formula: $R = \rho\frac{L}{A}$
  • L = length of resistor
  • A = cross sectional area
  • $\rho$ is a property called resistivity (measures how difficult for current to flow through it). Good conductors such as metal have low resistivity and insulators such as rubber have high resistivity

Voltage

• River, Voltage analogy: A river cannot flow if it is flat. Rivers flow from high to low ground. Voltage is the mountain that gives the river the height it needs to flow.
• Voltage is what creates currents
• A circuit usually gets voltage from a battery

Electric Circuits

• If a current always travels in the same direction through the pathway, it is known as a direct current
• Voltage must provide an electromotive force(emf) to drive the flow of charge
  • Emf is not a force, instead it is the work done per unit charge, measured in volts

Journey of Charge Through a Circuit

• Charge starts at the positive terminal of a battery and enters a wire and is pushed through by the electric field
• It then encounters resistance by the atoms and free electrons
• The resistance causes some of the electrical potential energy to turn into heat
• Then the voltage must do positive work on the charge to keep current going
• The charge then moves from negative to positive terminal and the journey starts again in the circuit

Energy and Power

• Rate electrical energy is transferred: $P = IV$
  • $V = IR$ (equation we discussed previously)
  • $P = IV = I(IR) = I^2R$
  • $P = IV = \frac{V}{R} \times V = \frac{V^2}{R}$

Circuit Analysis

• Resistors are symbolized by
• Batteries are symbolized by:
  • Longer line represents positive (higher potential) terminal and shorter represents negative (lower potential) terminal
• Basic Circuit Diagram:

Combination of Resistors

• Series (one after another):
• Parallel (side-by-side):
• Can be applied to more than one (not just 2) resistor in series: $R<em>s = \sum R</em>i$
• Can be applied to more than one (not just 2) resistor in parallel: $\frac{1}{R<em>p} = \sum \frac{1}{R</em>i}$

Kirchhoff’s Rules

• First Law (Junction/Node rule): The total current that enters a junction must equal the total current that leaves the junction
• Second Law (Loop Rule): The sum of potential differences (positive and negative) that traverse any closed loop in a circuit must be zero
  • When going across a resistor in the same direction as the current. The potential drops by IR
  • When going across a resistor in the opposite direction from the current, the potential increases by IR
  • When going from the negative to the positive terminal of a source of emf, the potential increases by V
  • When going from the positive to the negative terminal of a source of emf, the potential decreases by V