Current Electricity

Current Electricity shifts the focus from static charges to charges in motion. The chapter begins by defining electric current as the rate of flow of charge and introduces the concepts of drift velocity and current density. The core relationship explored is Ohm's Law, which connects the potential difference across a conductor to the current flowing through it via its resistance. You will learn about resistivity, the material property that determines resistance, and how temperature affects it.

The next part deals with building and analyzing circuits. This involves calculating the equivalent resistance for resistors connected in series and parallel, and similarly, understanding how to combine electrical cells. These principles allow you to determine the current, voltage, and power dissipated in different parts of a simple DC circuit.

The chapter then provides powerful tools for analyzing more complex networks. Kirchhoff's laws (the junction rule and the loop rule) are fundamental for solving circuits that cannot be simplified by series-parallel combinations. This is often the most challenging part, requiring careful application of sign conventions. Finally, you will study the principles and applications of measuring instruments like the Wheatstone bridge, metre bridge, and potentiometer. A good grasp of potential difference from the Electrostatics chapter is essential here.

Formulas for Current Electricity

Electric Current: $I = \frac{dQ}{dt}$ I is current, Q is charge, t is time.
Current and Drift Velocity: $I = n e A v_d$ n is number density of charge carriers, A is area, v_d is drift velocity.
Ohm's Law: $V = IR$ V is potential difference, I is current, R is resistance.
Resistance and Resistivity: $R = \rho \frac{l}{A}$ ρ is resistivity, l is length, A is cross-sectional area.
Temperature Dependence of Resistance: $R_T = R_0 [1 + \alpha(T - T_0)]$ α is the temperature coefficient of resistance.
Electrical Power: $P = VI = I^2 R = \frac{V^2}{R}$ P is power dissipated in a resistive component.
Resistors in Series: $R_{eq} = R_1 + R_2 + \dots$ For resistors connected end-to-end.
Resistors in Parallel: $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots$ For resistors connected across the same two points.
Kirchhoff's Junction Rule: $\sum I = 0$ At any junction, the algebraic sum of currents is zero.
Kirchhoff's Loop Rule: $\sum \Delta V = 0$ The algebraic sum of potential changes around any closed loop is zero.
Terminal Voltage of a Cell: $V = \mathcal{E} - Ir$ For a discharging cell, where E is e.m.f. and r is internal resistance.
Wheatstone Bridge Balance Condition: $\frac{R_1}{R_2} = \frac{R_3}{R_4}$ Condition for zero current through the galvanometer in the bridge.