Question

A heater coil is to be constructed with a nichrome wire (rho = 1.0 × 10−6 Ωm) that can operate at 500 W when connected to a 250 V supply. (a) What would be the resistance of the coil? (b) If the cross-sectional area of the wire is 0.5 mm2, what length of the wire will be needed? (c) If the radius of each turn is 4.0 mm, how many turns will be there in the coil?

Answer 1

(a)The resistance of the coil would be 125 Ω.

(b) The length of the wire whose cross-sectional area is 0.5 mm2 is 62.5m.

(c) The number of turns, the coil has is approximately 2500.

Explanation:

• Consider that the coil’s resistance is R.
• When connected across a supply, the power P consumed by the coil with resistance R is shown as $P=V 2 R \Rightarrow R=V 2 P \Rightarrow R=2502500=125 \Omega$
• It is known that $\mathrm{R}=\rho \mathrm{lA} \Rightarrow \mathrm{I}=125 \times 0.5 \times 10-610-6=62.5 \mathrm{m}$
• Let n denote the coil’s no. of turns. Then,$\mathrm{I}=2 \pi \mathrm{rn} \Rightarrow \mathrm{n}=62.52 \times 3.14 \times 4 \times 10-3 \approx 2500$