Q85 / 90 · JEE Main 2021 (25 Jul Shift 2) · Physics

Two circuits are shown in figure $(a)$ and $(b)$ . At a frequency of _______ $rad s^{- 1}$ the average power dissipated in one cycle will be the same in both the circuits.

Correct answer: 500

Solution

For figure $(a)$

$P_{avg} = \frac{V_{rms}^{2}}{R}$

$\frac{v_{rms}^{2}}{Z^{2}} \times R = \frac{v_{rms}^{2}}{R} \times 1$

$R^{2} = Z^{2}$

$25 = {(\sqrt{{(x_{C} - x_{L})}^{2} + 5^{2}})}^{2}$

$25 = {(x_{c} - x_{L})}^{2} + 25$

$x_{c} = x_{L} \Rightarrow \frac{1}{ω C} = ω L$

$ω^{2} = \frac{1}{L C} = \frac{10^{6}}{0.1 \times 40}$

$ω = 500$

Hence, the correct answer is 500.