Question 231: AC fundamentals

Question

Two circuits are shown in the figure (a) & (b). At a frequency of ____________ rad/s the average power dissipated in one cycle will be same in both the circuits.

Accepted Answer

For figure (a)
$${P_{avg}} = {{v_{rms}^2} \over R}$$
$${{v_{rms}^2} \over {{Z^2}}} 	imes R = {{v_{rms}^2} \over R} 	imes 1$$
$${R^2} = {Z^2}$$
$$25 = {\left( {\sqrt {{{({x_C} - {x_L})}^2} + {5^2}} } ight)^2}$$
$$ = 25{({x_C} - {x_L})^2} + 25$$
$${x_C} = {x_L} \Rightarrow {1 \over {\omega C}} = \omega L$$
$${\omega ^2} = {1 \over {LC}} = {{{{10}^6}} \over {0.1 	imes 40}}$$
$$\omega  = 500$$

AC fundamentals

Two circuits are shown in the figure (a) & (b). At a frequency of ____________ rad/s the average power dissipated in one cycle will be same in both the circuits.

Integer / Numeric Answer Type