Resitance, Ohm's Law, and Kirchhoff's Rules

AP Physics 2

Current

rate of flow of electric charge through a cross-sectional area (I)

Current Equation I =

Q/t

Current Unit

Amps / Amperes (A)

Current Conversion Rate

1 A = 1 C/s

Current Direction

Current flows towards positive charge

What causes I

Force of E

Drift Velocity

Average movement of electrons in circuit. Opposite of force E and opposite of current

n

Number density of charge carriers

Q/t = qnAv

Current

I = qnAvt

Relationship between current and drift velocity

What direction does force E point

decreasing potential

Resistance

Ratio of potential drop to the current

Resistance Equation

V/I

Resistance Conversion: 1 ohm =

1 V/A

Ohm’s Law

I is directly proportional to V and inversely proportional to R

Ohm’s Law Equation

V = IR (R constant)

Ohmic graphs are

linear

Nonohmic graphs are

non linear

Wire Resistance Equation

R = p x L/A

Resistance in a wire is proportional to

length

Resistance in a wire is inversely proportional to

cross-sectional area

p

resistivity of conducting material

What unit is wire resistivity measured in

Ohm-meters

Resistivity is largely dependent on

T

Rate of Energy Loss Equation

-U/-t = Q/t x V = IV

P = VI

energy loss per unit of time is power dissipated from conducting segment

P Units

Watts

Power Dissipated in a Resistor (Equation)

P = V² / R

Electromotive Force

provided by battery to generate electric field

What does the emf source do to a charge

work is done, raising potential energy

Work per unit of charge

emf

EMF Units

Volts

Resistors in Series

carry the same current

Resistors in Series Equation

R(eq) = R(1) + R(1) + R(1) + …

Parallel Resistors

have the same potential difference across them

Parallel Resistors Equation

R(eq) = 1/R(1) + 1/R(1) + 1/R(1) + …

Kirchhoff's Rules

Loop and Junction

Loop Rule

Net change in potential must be zero

Junction Rule

If I1 splits into I2 and I3 then I2 + I3 must equal I1

RC Circuit

contains a resistor and a capacitor

Ohm’s Law

I is directly proportional to V and inversely proportional to R

Capacitance Equation

C = Q/V

Unit of Capacitance

Farad

Permittivity of Free Space ( e0)

8.85 × 10^-12 F/m = 8.85 pF/m

Micro Farad

1 uF = 10^-6 F

Pico Farad

1 pF = 10 ^-12 F

Permittivity of Free Space Unit

Farad per meter

Capacitance Equation for Sphereical Capacitors

C = 4(pie)(e0)R

What does not matter for capacitance

charge

Potential Difference Equation (V)

= E x d

Capacitance Equation

= Q / V = (e0)A / d

Capacitance is proportional to

area of plates

Capacitance is inversely proportional to

plate seperation distance

Q in a capacitor will equilibrate when

its potential difference is equal to the potential energy of the battery terminals

U

total energy stored in a capacitor

Energy Stored in a Capacitor Equation

½ x QV = ½ X CV²