(a) List the factors on which the resistance of a uniform cylindrical conductor of a given material depends.

(b) The resistance of a wire of $0.01\text{ cm}$ radius is $10\Omega$. If the resistivity of the wire is $50 \times 10^{-8}\Omega\text{ m}$, find the length of this wire.

OR

(a) Electric Power: Electric power is the rate at which electrical energy is consumed or dissipated in an electric circuit.

$$\text{Power } (P) = \frac{\text{Work Done } (W)}{\text{Time } (t)} = VI$$

SI Unit: The SI unit of electric power is watt (W). One watt is the power consumed by a device that carries $1\text{ A}$ of current when operated at a potential difference of $1\text{ V}$.

(b) Calculation of Energy Consumed:

Given:

• Power of the kettle, $P = 2\text{ kW}$
• Time of use, $t = 2\text{ h}$

(i) In kilowatt-hour (kWh):

$$\text{Energy } (E) = \text{Power } (P) \times \text{Time } (t)$$

$$E = 2\text{ kW} \times 2\text{ h} = 4\text{ kWh}$$

(ii) In Joules (J):

We know that $1\text{ kWh} = 3.6 \times 10^6\text{ J}$.

$$E = 4 \times 3.6 \times 10^6\text{ J}$$

$$E = 14.4 \times 10^6\text{ J} = 1.44 \times 10^7\text{ J}$$

Therefore, the energy consumed is $4\text{ kWh}$ or $1.44 \times 10^7\text{ J}$.