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.
Answer & explanation
Correct answer: option 1
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