Current Electricity
How charges flow through conductors — from Ohm's law to Kirchhoff's rules
Table of Contents
3.1 Introduction
In Chapter 1, all charges whether free or bound, were considered to be at rest. Charges in motion constitute an electric current. Such currents occur naturally in many situations — lightning is one such phenomenon. In our everyday life we see many devices where charges flow in a steady manner, like water flowing smoothly in a river.
3.2 Electric Current
Electric current is the rate of flow of charge through a cross-section:
3.3 Ohm's Law
At constant temperature, the current through a conductor is directly proportional to the potential difference across it:
Ohm's law is obeyed by metals and most conductors at constant temperature. Non-ohmic devices (diodes, transistors, electrolytes) have non-linear V-I characteristics and do not obey V = IR.
3.4 Resistance and Resistivity
Resistance depends on the geometry of the conductor and the material property called resistivity:
Resistors in Series
R = R₁ + R₂ + ...
Same current through each. Voltages add. Total resistance increases.
Resistors in Parallel
1/R = 1/R₁ + 1/R₂ + ...
Same voltage across each. Currents add. Total resistance decreases.
3.5 Temperature Dependence
Resistivity increases with temperature for metals:
3.6 Kirchhoff's Laws
Two fundamental laws for analyzing complex circuits:
Kirchhoff's Current Law (KCL)
ΣI = 0 at any junction. Current entering = current leaving. Based on conservation of charge.
Kirchhoff's Voltage Law (KVL)
ΣV = 0 around any closed loop. Sum of potential drops = sum of EMFs. Based on conservation of energy.
3.7 Wheatstone Bridge
A circuit to measure unknown resistance using four resistors in a bridge configuration. At balance:
3.8 Potentiometer
A potentiometer compares EMFs and measures internal resistance. It works on the principle that for a constant current, the potential drop across a wire is proportional to its length: