ch 10

Electromotive Force (emf)

A special type of potential difference representing work done per unit charge when no current flows.

Emf Source

A charge pump, such as a battery, that uses energy from chemical reactions to move charges and maintain a potential difference.

Ideal Battery

An emf source with no internal resistance, maintaining constant terminal voltage equal to the emf.

Terminal Voltage (V_terminal)

The voltage measured across a battery's terminals, calculated as V_terminal = ε - Ir.

Internal Resistance (r)

The resistance within a battery that causes the terminal voltage to decrease as current increases.

Depletion of Battery

The increase of internal resistance as the battery is used up due to oxidation of plates or reduced electrolyte acidity.

Current (I) Calculation

Determined by the total resistance in the circuit: I = ε / (r + R).

Battery Charger Voltage Requirement

Must exceed the battery's emf to reverse the current direction and replenish chemical potential.

Electron Flow Direction

Electrons flow opposite to conventional current, moving from negative to positive terminal.

Resistor Function

Limits charge flow in a circuit, governed by Ohm’s Law: V = IR.

Equivalent Resistance in Resistor Circuit

Depends on individual resistor values and their connection type (series, parallel, combination).

Series Circuit Features

1. Same current flows through each resistor. 2. Equivalent resistance is the sum of individual resistances (R_S = R_1 + R_2 + … + R_N). 3. Voltage divides among resistors.

Parallel Circuit Features

1. Same potential drop across each resistor. 2. Total current divides among resistors; sum of individual currents equals total current. 3. Equivalent resistance is less than the smallest individual resistance.

Series Equivalent Resistance Formula

R_S = ΣR_i for resistors in series.

Parallel Equivalent Resistance Formula

R_P = (Σ(1/R_i))^(-1) for resistors in parallel.

Junction Rule

The sum of currents entering a junction equals the sum of currents leaving the junction: ΣI_in = ΣI_out.

Junction Definition

A connection of three or more wires in a circuit.

Kirchhoff's First Rule (Junction Rule)

ΣI_in = ΣI_out, stating current conservation at a junction.

Physical Principle of Junction Rule

Conservation of charge; charge flowing into a junction must flow out.

Kirchhoff's Second Rule (Loop Rule)

ΣV = 0; the algebraic sum of potential changes around a closed loop must equal zero.

Physical Principle of Loop Rule

Conservation of energy; energy supplied must equal energy lost in a loop.

Potential Change Across Resistor (Same Direction)

Subtract potential drop (-IR) when moving in the same direction as current.

Potential Change Across Resistor (Opposite Direction)

Add potential drop (+IR) when moving against the direction of current.

Potential Change Across Voltage Source (Negative to Positive)

Add potential drop (+V) when moving from the negative to positive terminal.

Potential Change Across Voltage Source (Positive to Negative)

Subtract potential drop (-V) when moving from positive to negative terminal.

RC Circuit Definition

An electrical circuit containing resistance (R) and capacitance (C) where the capacitor stores energy.

Charge on Capacitor at t = ∞

Charge approaches maximum value Q = Cε as time increases during charging.

Time Constant (τ) Definition

τ = RC; the time required for a capacitor to charge to 63.2% of maximum, measured in seconds.

Current Behavior in Charging Circuit

Current is maximum at t = 0 (I_0 = ε/R) and decreases exponentially toward zero as capacitor charges.

Discharge Circuit Voltage Source Behavior

Voltage source is removed, allowing capacitor charge to flow through the resistor.

Charge on Capacitor During Discharge

Charge decreases exponentially from initial charge: q(t) = Qe^{-t/τ}.

Negative Sign in Discharging Current Formula

Indicates current flows in the opposite direction to charging current.