Question

(A) (i) Define electric power. Express it in terms of potential difference (V) and resistance (R).
(ii) 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:
(a) power rating of the oven
(b) current drawn by the oven
(c) resistance of the oven when it is red hot

OR

(B) (i) Write the relation between resistance R and electrical resistivity ρ of the material of a conductor in the shape of a cylinder of length 𝑙 and area of cross-section A. Hence derive the SI unit of electrical resistivity.
(ii) The resistance of a metal wire of length 3 m is 60 Ω. If the area of cross-section of the wire is \(4 \times 10^{-7}\) m², calculate the electrical resistivity of the wire.
(iii) State how would electrical resistivity be affected if the wire (of part ‘ii’) is stretched so that its length is doubled. Justify your answer.

Answer 1

(i). Electric power quantifies the rate of electrical energy consumption or transformation into other energy forms.
          Formula: \( P = \frac{V^2}{R} \), with \( P \) representing power, \( V \) potential difference, and \( R \) resistance.

(ii). Oven Power Rating: 
\[ \text{Energy consumed over 5 hours} = 11 \, \text{units (1 unit = 1 kWh)} = 11000 \, \text{Wh} \] \[ \text{Power rating, } P = \frac{\text{Energy consumed}}{\text{Time}} = \frac{11000}{5} = 2200 \, \text{W} \] 
Oven Current Draw: \[ P = VI \implies I = \frac{P}{V} = \frac{2200}{220} = 10 \, \text{A} \] 
Oven Resistance (at red hot): \[ R = \frac{V^2}{P} = \frac{220^2}{2200} = 22 \, \Omega \]

---

(i). \[ R = \rho \frac{l}{A}, \, \text{where } \rho = \frac{RA}{l} \]
          SI Unit of Resistivity: \[ \rho = \frac{\text{Resistance} \times \text{Area}}{\text{Length}} = \frac{\Omega \times m^2}{m} = \Omega\cdot m \]

(ii). \[ \rho = \frac{R \times A}{l} = \frac{60 \times 4 \times 10^{-7}}{3} = 8 \times 10^{-6} \, \Omega \cdot m \]

(iii).Electrical resistivity is an intrinsic material property, independent of the conductor's dimensions. Stretching a wire does not alter its resistivity, as this property is determined solely by the material composition, not its physical form or size.