Power Consumed in an Electrical Circuit

A battery is connected to an external resistor R. The positive charges flow in the direction of the current in the resistor and from negative to positive terminal inside the battery. The potential difference between two points gives kinetic energy to the charges. These moving charges collide with the atoms (ions) in the resistor and thus lose a part of their kinetic energy. This energy increases with the temperature of the resistor. The loss of energy by moving charges is made up at the expense of chemical energy of the battery.

The rate of loss of potential energy by moving charge ∆Qin going through the resistor is

∆U/∆t = V ∆Q/∆t = VI

where I is the current in the circuit and V is potential difference between the ends of the resistor. It is assumed that the resistance of the connecting wires is negligible. The total loss is in the resistor R only. Rate of loss of energy is defined as power.

P = VI

Since, V = IR

P = I²R = V²/R

The SI unit of power is watt (W).

The electrical power lost in a conductor as heat is called joule heat. The heat produced is proportional to:

• (i) square of current (I)
• (ii) resistance of conductor (R)
• (iii) time for which current is passed (t)

The statement Q = I²Rt, is called Joule’s law for heating effect of current.