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(a) The resistance of a wire of $0.01\ \text{cm}$ radius and $1.0\ \text{cm}$ length is $7\ \Omega$. Calculate its resistivity.
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(a) $r = 0.01 \text{ cm}=1 \times 10^{-4} \text{ m}$
$l = 1 \text{ cm} = 0.01 \text{ m}$
$R=\rho \frac{l}{A}$
$\rho = \frac{RA}{l} = \frac{R \times \pi r^2}{l}$
$\rho = \frac{7 \times 22 \times 10^{-8}}{7 \times 0.01}$
$\rho = 22 \times 10^{-8} \times 10^2$
$\rho = 22 \times 10^{-6} \Omega m =2.2 \times 10^{-5} \Omega m$ (1)
(b) Resistance of electric heater $R = \frac{V}{I}$
$R = \frac{220}{11}$
$R = 20 \Omega$ (½)
$P = \frac{V^2}{R}$
$P = \frac{200 \times 200}{20}$
$P = 2000\text{W}/2 \text{ kW}$ (½)
$l = 1 \text{ cm} = 0.01 \text{ m}$
$R=\rho \frac{l}{A}$
$\rho = \frac{RA}{l} = \frac{R \times \pi r^2}{l}$
$\rho = \frac{7 \times 22 \times 10^{-8}}{7 \times 0.01}$
$\rho = 22 \times 10^{-8} \times 10^2$
$\rho = 22 \times 10^{-6} \Omega m =2.2 \times 10^{-5} \Omega m$ (1)
(b) Resistance of electric heater $R = \frac{V}{I}$
$R = \frac{220}{11}$
$R = 20 \Omega$ (½)
$P = \frac{V^2}{R}$
$P = \frac{200 \times 200}{20}$
$P = 2000\text{W}/2 \text{ kW}$ (½)