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PhysicsEMI/ACSeries AC CircuitsHard2 minPYQ_2021

PhysicsHardnumerical

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.

Answer:

500.00

Solution:

For figure $(a)$

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

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

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

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

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

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

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

$ω = 500$

Stream:JEESubject:PhysicsTopic:EMI/ACSubtopic:Series AC Circuits

⏱ 2mℹ️ Source: PYQ_2021

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