Nichrome wire of length 10 m is used to make a heating coil. This coil consumes power of 160 W when there is a potential difference of 40 V across it. Find the diameter of this wire. Resistivity of Nichrome is 10^–6 Ω m.

1.128 mm

The correct answer is Option (1) → 1.128 mm

Electric power is given by

$P=\frac{V^2}{R} \Rightarrow P=160 W, V = 40 V \Rightarrow R=10 \Omega$

Also, $R=\frac{\rho l}{A} \Rightarrow 10=\frac{10^{-6} \times 10}{A} \Rightarrow A=10^{-6} ~m^2$

$\Rightarrow \pi r^2=10^{-6} \Rightarrow r^2=\frac{10^{-6}}{\pi}$

$\Rightarrow r=0.564 \times 10^{-3}$

⇒  diameter,  $d = 2 r=1.128 \times 10^{-3}$ = 1.128 mm