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A 2000 Hz, 20 volt source is connected to a resistance of 20 ohm, an inductance of 0.125/ $π$ H and a capacitance of 500/ $π$ nF all in series. Calculate the time (in seconds) in which the resistance (thermal capacity = 100 joule/ $\circ_{C}$ ) will get heated by 10 $°$ C. (Assume no loss of heat)

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answer is 50.

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Detailed Solution

$power (P) = I_{rms}^{2} R$ $P = {[\frac{20}{\sqrt{R^{2} + {(ω L - \frac{1}{ω c})}^{2}}}]}^{2} \times R$

$where ω = 2 \times π \times 2000$

$Δ H = (ms) Δ θ = P (Δ t) \Rightarrow Δ t = \frac{(ms) Δ θ}{P} = \frac{100 \times 10}{P} = 50 \sec$

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