Question 203: AC fundamentals

Question

Find the peak current and resonant frequency of the following circuit (as shown in figure).

Accepted Answer

We know, z = $$\sqrt {{{({x_L} - {x_C})}^2} + {R^2}} $$
$${x_L} = {\omega _L} = 100 	imes 100 	imes {10^{ - 3}} = 10\Omega $$
$${x_C} = {1 \over {{\omega _C}}} = {1 \over {100 	imes 100 	imes {{10}^{ - 6}}}} = 10\Omega $$
$$ 	herefore $$ $$z = \sqrt {{{(10 - 100)}^2} + {R^2}}  = \sqrt {{{90}^2} + {{120}^2}} $$
$$ = 30 	imes 5 = 150\Omega $$
$${i_{peak}} = {{\Delta v} \over z} = {{30} \over {150}} = {1 \over 5} amp = 0.2$$ amp
For resonant frequency,
$$  \omega L = {1 \over {\omega C}} \Rightarrow {\omega ^2} = {1 \over {LC}} \Rightarrow \omega  = {1 \over {\sqrt {LC} }}$$
& $$f = {1 \over {2\pi \sqrt {LC} }} = {1 \over {2\pi \sqrt {100 	imes {{10}^{ - 3}} 	imes 100 	imes {{10}^{ - 6}}} }}$$
$$ = {{100\sqrt {10} } \over {2\pi }} = {{100\pi } \over {2\pi }} = 50$$ Hz
as $$\sqrt {10}  \approx \pi $$

Answer

2 A and 100 Hz

Answer

2 A and 50 Hz

Answer

0.2 A and 100 Hz

Answer

0.2 A and 50 Hz

AC fundamentals

Find the peak current and resonant frequency of the following circuit (as shown in figure).

Choose the correct answer: