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A  750 H_{2}, 20V(rms) source is connected to a ressitance of 100\Omega an inductance of 0.18034 and a capacitance of 10 \mu F all in series. The time (in seconds) in which the resistance ( heat capacity 2J/^{\circ}C) will get heated by  10^{\circ}C (assume no loss of to the surrounding) is close to
 
Option: 1 348
Option: 2 245
Option: 3 365
Option: 4 418

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\begin{array}{l} \omega=2 \pi \times 750 =1500 \pi \\ \mathrm{R}=100 \Omega, \mathrm{L}=0.1803 \mathrm{H}, \mathrm{C}=10 \mu \mathrm{F} \\ \begin{array}{l} \mathrm{z}=\sqrt{100^{2}+\left(\omega \mathrm{L}-\frac{1}{\omega \mathrm{c}}\right)^{2}} =834 \Omega \end{array}\\ \\ \mathrm{I_{rms}}=\frac{V_{rms}}{Z}=\frac{20}{834}=0.024 \mathrm{A} \\ \\ \text { P }=I_{rms} \times V_{rms} \times cos \theta=0.024 \times 20 \times \frac{R}{Z}=0.058\\ Now,\ P \times t=S \Delta \theta \\ Here \ S =thermal\ capacity\\ \\ \therefore t=\frac{S \Delta \theta}{ P}=\frac{2 \times 10}{0.058}=348 s \end{array}

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