Unit 11 Physics C

Current

flow of charge per unit time trough an area; when a potential difference is applied across a circuit, current will flow

Current as a Function of Time

I=Q/dt=dq/dt

Drift Velocity

net motion of electric charge carriers in a wire; e.g. if 10 particles to right and 14 to left, overall the motion of particles "drifts" to left

+

net velocity of all individual charge velocities moving in a wire

Important Notes for v_d

Speed of each charged particle is much greater than drift speed

+

e.g. two electrons move 30m/s; one moves -30 m/s; drift velo = (60-30)/3=10 m/s

+

e.g. if one electron moving right and one moving left, no drift velocity

Current as a Function of Drift

I=nq(vd)A, where n is number of charges per cubic meter of volume, q is the quantity of charge, vd is drift velocity, and A is cross-sectional area of wire

Electric Current Density (J)

J=I/A (A/m^2)

J=nqv_d

Current Density Vector

if charges are positive, direction is same; if charges are negative, directoin switches

Current as Function of Density

I=JA

E-Field and Current and Resistivity

the greater the E-Field, the greater the electric current density

the greater the resistivity, the lower the electric current density

E=pJ

Conventional Current

electric current in a wire based on the movement of positive charges

Resistance

the opposition of charges moving through a circuit

Resistors

clog up current, but charges speed up within resistor, creating more collisions and transforming energy from circuit

Resistance Equation

R=pl/A, where p is resistivity, l is wire length, and A is cross-sectional area

Resistivity (p)

inverse of resistivity is conductivity

Series Circuit

if charges flowing through the circuit only have one path to move

Parallel Circuit

if there is a junction or intersection

Limitations of Ohm's Law

Non-Ohmic Materials + Temperature Dependency + AC Circuits/Frequency Dependency + Very High Frequencies

Power

rate of energy dissipation or transformation

P=(qdV)/dt=IV

Power and Bulbs

adding more bulbs in series, decreases brightness and total power

Short Circuit

charges take path of least resistance, and so if a wire is put in before another light bulb, functionally no charge will go through that bulb

Resistors in Series

Current only has ONE path to travel

Current is same for all resistors on the path

R_eq = sum of individual resistance

Resistors in Parallel

Current has multiple paths it could travel

Potential difference is same across all resistors in the combo

More paths = less equivalent resistance

Ideal Battery

Terminal Voltage is same as EMF; negligible internal resistance

Non-Ideal Battery

Terminal Voltage = EMF-Ir, where r is internal resistance

Ideal Wires

if a wire is a good conductor, its resistance is much smaller than the load, so it's usually neglected

ONLY NEGLECTED IF THERE'S A LOAD

Ammeter

A tool used to measure current at a specific point in a circuit

Connected in series, so ideally have zero resistance

Voltmeter

a tool used to measure voltage between two points in a circuit

must be connected in parallel with element across which voltage is being measured; ideally have infinite resistance

Kirchhoff's Loop

Complete loop around a circuit has a potential difference of zero; Summation of Delta V = 0

Kirchhoff's Junction Rule

The current going into a junction must equal the current going out

Capacitors in Series

More capacitors on path means less capacitance

Current is same for all capacitors, so CHARGE is same

Capacitors in Parallel

More capacitors means more capacitance

Voltage is same across all capacitors

Voltage Across a Charge Capacitor

Vc(t) = Vb(1-e^-t/RC)

Charge on Charging Capacitor

Q=CV_b*(1-e^-t/RC)

Voltage Across Resistor When Charging Capacitor

V=V_b*e^-t/RC

Current through Resistor When Charging Capacitor

I=(V_b/R)*e^-t/RC

Voltage Across Discharging Capacitor + Resistor When Discharging Capacitor

V=V_b*e^-t/RC

Charge on Discharging Capacitor

Q=Q_o*e^-t/RC

Current Through Resistor When Discharging Capacitor

I(t)=-V_b/R * e^-t/RC

Uncharged Capacitors

act as wires initially until charge builds up

Fully Charged Capacitors

act as roadblocks

RC Time Constant (Tau)

Measure of how quickly the capacitor will charge/discharge

Tau = Req * Ceq

Tau for Charging Capacitor

Value of tau as measure of time tells us when we have gained 63% of max charge

Tau for Discharging Capacitor

Value of tau as measure of time tells us when we have lost 63% of max charge (i.e. 37% of max charge left)

e^-t/RC vs 1-e^-t/RC

Decaying to Zero vs Approaching a Maximum