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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?
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Solution
(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,
\[l = 2\pi rn\]
\[ \Rightarrow n = \frac{l}{2\pi r}\]
\[ \Rightarrow n = \frac{62 . 5}{2 \times 3 . 14 \times 4 \times {10}^{- 3}} \approx 2500\]
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