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QPages 218-219: Q4: HC Verma: Concepts of Physics - Volume 2 Thermal and Chemical Effects of Electric Current Pages 218-219: Q4 Solution: A heater coil is to be constructed with a nichrome wire ) that…

A heater coil is to be constructed with a nichrome wire ρ=1.0×10−6 Ωm\rho = 1.0 \times 10^{-6} \ \Omega\text{m}) 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 mm20.5 \text{ mm}^2, 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?

Step-by-Step Verified Solution

**Answer:** (a) R=125 ΩR = 125\ \Omega (b) l=62.5l = 62.5 m (c) n≈2500n \approx 2500 turns. **Step-by-Step Explanation:** (a) R=V2/P=2502/500=125 ΩR = V^2/P = 250^2/500 = 125\ \Omega. (b) R=ρl/A⇒l=RA/ρ=(125×0.5×10−6)/(1.0×10−6)=62.5R = \rho l/A \Rightarrow l = RA/\rho = (125 \times 0.5 \times 10^{-6})/(1.0 \times 10^{-6}) = 62.5 m. (c) Circumference per turn =2πr=2π(0.004)=0.0251= 2\pi r = 2\pi(0.004) = 0.0251 m. n=62.5/0.0251≈2500n = 62.5/0.0251 \approx 2500 .

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