Question

(a) What is meant by " electric power"? Write the formula for electric power in terms of potential difference and current.
(b) The diagram below shows a circuit containing a lamp L, a voltmeter and an ammeter,. The voltmeter reading 3 V and the ammeter reading is 0.5 A.


(i) What is the resistance of the lamp?
(ii) What is the power of the lamp?

(c) Define kilowatt-hour. How many joules are there in one kilowatt-hour?
(d) Calculate the cost of operating a heater of 500 W for 20 hours at the rate of Rs 3.90 per unit.

Answer 1

(a) Electrical power is the electric work done per unit time.
In terms of potential difference and current, electric power is given as:
Electric power, P = potential difference, V x current, I
P = VI

(b) Given:
Potential difference = reading of the voltmeter, V = 3 V
Current in the circuit = reading of the ammeter, I= 0.5 A
(i) Resistance of the lamp, R = $\frac{\mathrm{V}}{\mathrm{I}}=\frac{3\mathrm{V}}{0.5\mathrm{A}}=6\mathrm{ohm}$
(ii) Power, P = VI = 3 V x 0.5 A = 1.5 W

(c) One kilowatt-hour is the amount of electrical energy consumed when an electrical appliance having a power rating of one kilowatt is used for one hour.

1 kilowatt-hour = 36,00,000 joules

(d) Power rating of the heater, P = 500 W
Duration of the operation, t = 20 hours
Electrical energy consumed = P x t
= 500 W x 20 hours
= 10000 W = 10 kW
Rate for 1 kW = Rs. 3.90
Total cost of operating = units consumed x rate = 10 x Rs. 3.90 = Rs. 39