First slide

Parallel L-C-R circuit

Question

In the net work shown if $X_{C} = \frac{R}{\sqrt{2}} a n d X_{L} = R,$ ratio of power consumed in the upper branch to that in the lower branch is

Difficult

A

3 : 5
B

5 : 4
C

4 : 3
D

2 : 3

Solution

(3)
$P_{C} =$ Power consumed in the upper branch
$= \frac{V_{m}^{2} R}{2 (R^{2} + X_{C}^{2})} = \frac{V_{m}^{2} R}{2 (R^{2} + \frac{R^{2}}{2})} = \frac{V_{m}^{2}}{3 R}$
$P_{L} =$ Power consumed in the lower branch
$\begin{array}{l} = \frac{V_{m}^{2} R}{2 (R^{2} + X_{L}^{2})} = \frac{V_{m}^{2} R}{2 (R^{2} + R^{2})} = \frac{V_{m}^{2}}{4 R} \\ ∴ \frac{P_{C}}{P_{L}} = \frac{4}{3} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App