Question

A heater coil is to be constructed with a nichrome wire (ρ = 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) Let R be the resistance of the coil.

The power P consumed by a coil of resistance R when connected across a supply V is given by

\[P = \frac{V^2}{R}\]

\[ \Rightarrow R = \frac{V^2}{P}\]

\[ \Rightarrow R = \frac{\left( 250 \right)^2}{500} = 125  \Omega\]

(b) We know:-

\[R = \rho\frac{l}{A}\]

\[ \Rightarrow l = \frac{RA}{\rho}\]

\[ \Rightarrow l = \frac{125 \times 0 . 5 \times {10}^{- 6}}{{10}^{- 6}} = 62 . 5  m\]

(c) Let n be the number of turns in the coil. Then,

\[l = 2\pi rn\]

\[ \Rightarrow n = \frac{l}{2\pi r}\]

\[ \Rightarrow n = \frac{62 . 5}{2 \times 3 . 14 \times 4 \times {10}^{- 3}} \approx 2500\]