Current Electricity: Resistance, Circuits, and Cells Lecture Notes

General physics vocabulary and principles regarding resistivity, conductivity, circuit combinations, cell properties, and fundamental electrical laws based on the provided notes.

Resistivity (ρ)

A material constant used to calculate resistance for a specific material; copper wires of different lengths and cross-sections will have the same resistivity but different resistance.

SI Unit of Resistivity

$$\Omega\,m$$

Conductance ($G$)

The reciprocal of resistance, defined as $G = \frac{1}{R}$. Its S.I. unit is the Siemens ($S$) or mho.

Conductivity ($\sigma$)

The reciprocal of resistivity ($1/\rho$), expressed microscopically as $\sigma = \frac{ne^2\tau}{m}$.

Microscopic form of Ohm's Law

The relationship given by the equation $J = \sigma E$, where $J$ is current density, $\sigma$ is conductivity, and $E$ is electric field.

Resistance change due to stretching

When a wire is stretched so its length increases by $n$ times while volume remains constant, the new resistance becomes $R' = n^2 R$; if the radius decreases by $n$ times, new resistance becomes $R' = n^4 R$.

Temperature coefficient of resistance ($\alpha$)

The value representing the change in resistance for every unit increase in temperature; it is large and positive for metals and negative for semiconductors like Silicon and Germanium.

Alloys (Nichrome, Constantan, Manganin)

Materials with a small and positive $\alpha$, meaning their resistance change is small with temperature; used in laboratory equipment like Potentiometers and Meter bridges.

Superconductors

Materials that exhibit zero resistance at very low temperatures; for example, Mercury behaves as a superconductor at $4.2\,K$.

Series Combination of Resistors

A configuration where the current $I$ through each resistor is the same but potential drop is different; effective resistance is $R_s = R_1 + R_2$.

Parallel Combination of Resistors

A configuration where the potential across each resistor is the same but current divides; effective resistance is $\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2}$.

EMF (Electromotive Force)

The maximum potential difference between two terminals of a cell when the cell is in an open circuit (not drawing any current).

Internal resistance ($r$)

The resistance offered to the flow of electrons between the terminals of a cell; it is affected by electrode separation, plate area, temperature, and ion concentration.

Terminal potential difference ($V$)

The potential difference between the terminals of a cell when it is in a closed circuit and drawing current, expressed as $V = E - Ir$ during discharging.

Short circuit

The condition where the external resistance ($R$) is zero ($R = 0$), leading to maximum current flow defined by $I = \frac{E}{r}$.

Charging of a cell

The condition where current enters the positive terminal, and terminal potential difference is greater than EMF, expressed as $V = E + Ir$.

Maximum Power Transfer Theorem

States that the power in a circuit is maximum when the effective internal resistance is equal to the external resistance ($R = r$).

Efficiency for maximum power transfer

The efficiency ($\eta$) of a cell when transferring maximum power is $50\%$.

Kirchhoff's Junction Rule

Based on the conservation of charge; it states that the algebraic sum of currents meeting at a junction is zero ($\sum I = 0$).

Kirchhoff's Loop Rule

Based on the conservation of energy; it states that the total change in potential across any closed loop involving cells and resistors is zero ($\sum \Delta V = 0$).

Wheatstone Bridge

A circuit of four resistors ($P, Q, R, S$) where the galvanometer shows null deflection ($I_g = 0$) if the ratio of resistors satisfies $\frac{P}{Q} = \frac{R}{S}$.

Meter Bridge

A practical application of the Wheatstone Bridge used to determine unknown resistance; its wire is typically made of alloys like Nichrome, Constantan, or Manganin.

Joule's Law

States that the heat developed in a resistor is proportional to the square of the current, the resistance, and the time: $H = I^2 Rt$, with S.I. unit Joules ($J$).

Commercial Unit of Electrical Energy

$kWh$ (Kilowatt-hour), also known as 1 Unit, which is equal to $3.6 \times 10^6\,J$.