A 750 Hz, 20 V (rms) source is connected to a resistance of 100 Ω, and inductance of 0.1803 H and a capacitance of 10 μF all in series. The time in which the resistance (heat capacity 2 J/°C) will get heated by 10°C. (assume no loss of heat to the surroundings) is close to:
Answer & explanation
Correct answer: option 4
$\omega = 2\pi f = 1500\pi$
$ \text{Impedance z } = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2} = 834 \Omega$
$ I_{rms} = \frac{V_{rms}}{Z} = \frac{20}{834} = 0.024 A$
$\text{Power Factor} cos\phi = \frac{R}{Z} = \frac{100}{834}$
$\text{Power }P = V_{rms} I_{rms} cos\phi = 20\times 0.024 \times \frac{100}{834} = 0.058J/s $
$ Time = \frac{20}{0.058} = 348 Sec$