(a) Define electric power. Express it in terms of potential difference (V) and resistance (R).

(b) An electric oven is designed to work on the mains voltage of 220 V. This oven consumes 11 units of electrical energy in 5 hours. Calculate :

1. power rating of the oven
2. current drawn by the oven
3. resistance of the oven when it is red hot

(a) Electric power is the rate at which electrical energy is consumed or converted into other forms of energy such as heat, light or mechanical work in an electrical circuit.

It is given by :

$\text P = \text {VI}$

where

• $\text P$ = electric power,
• $\text V$ = potential difference,
• $\text I$ = current

Using Ohm’s law ($\text V = \text {IR}$),

$\text P = \text I^2 \text R = \dfrac{\text V^2}{\text R}$

Thus, electric power can also be expressed in terms of potential difference (V) and resistance (R) as:

$\dfrac{\text V^2}{\text R}$

(b) Given,

• Mains voltage ($\text V$) = 220 V
• Electrical energy consumed by the oven ($\text H$) = 11 units
• Time duration for operating the oven ($\text t$) = 5 hours

1. As

1 unit = 1 KWh

Then

$\text H$ = 11 units = 11 KWh

Also,

Power rating of the oven is given by,

$\text P = \dfrac {\text H}{\text t} \\[1em] = \dfrac{11}{5} \\[1em] \Rightarrow \text P = 2.2 \text { kW} \\[1em] \Rightarrow \text P = 2.2 \times 1000 \\[1em] \Rightarrow \text P = 2200\ \text W$

Hence, the power rating of the oven is 2200 W.

2. Current drawn by the oven is given by,

$\text I = \dfrac{\text P}{\text V} \\[1em] = \dfrac{2200}{220} \\[1em] \Rightarrow \text I = 10\ \text A$

Hence, the current drawn by the oven is 10 A.

3. Resistance of the oven is given by Ohm's law,

$\text R = \dfrac{\text V}{\text I} \\[1em] = \dfrac{220}{10} \\[1em] \Rightarrow \text R = 22\ \text Ω$

Hence, the resistance of the oven when it is red hot is 22 Ω.