A 750 Hz, 20 V (rms) source is connected to a resistance of 100 Ω, an inductance of 0.1803 H and a capacitance of 10 μF, all in series. The time in which the resistance (heat capacity 2J/°C) will get heated by 10°C. (Assume no loss of heat to the surroundings) is close to :
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Question

A 750 Hz, 20 V (rms) source is connected to a resistance of 100 Ω, an inductance of 0.1803 H and a capacitance of 10 μF, all in series. The time in which the resistance (heat capacity 2J/°C) will get heated by 10°C. (Assume no loss of heat to the surroundings) is close to :

Options

G1 Physics · Accepted Answer

At f=750 Hz, find Xₗ=2πfL and X꜀=1/(2πfC), then Z=√[R²+(Xₗ−X꜀)²]. With Iᵣₘₛ=20/Z, resistor power is P=Iᵣₘₛ²R. Heating by 10°C requires 20 J, giving t≈348 s. Hence option C.