A $750\ \text{Hz}$, $20\ \text{V (rms)}$ source is connected to a resistance of $100\ \Omega$, an inductance of $0.1803\ \text{H}$ and a capacitance of $10\ \mu\text{F}$ all in series. The time in which the resistance (heat capacity $2\ \text{J}/^\circ\text{C}$) will get heated by $10^\circ\text{C}$ (assume no loss of heat to the surroundings) is close to:
Answer: (D) $348\ \text{s}$
$X_L = 2\pi\times750\times0.1803 \approx 849.6\ \Omega$, $X_C = \dfrac{1}{2\pi\times750\times10^{-5}} \approx 21.2\ \Omega$.
$Z = \sqrt{100^{2} + 828.4^{2}} \approx 834\ \Omega$, $I_{rms} = \dfrac{20}{834} \approx 0.024$ A.
Power in the resistor: $P = I^{2}R \approx 0.0575$ W. Heat needed $= 2\times10 = 20$ J.
$$t = \frac{20}{0.0575} \approx 348\ \text{s}$$
Solution by Sreeraj P, M.Sc Physics