Question 172: AC fundamentals

Question

In a series resonant $$LCR$$ circuit, the voltage across $$R$$ is $$100$$ volts and $$R = 1\,k\Omega $$ with $$C = 2\mu F.$$ The resonant frequency $$\omega $$ is $$200$$ $$rad/s$$. At resonance the voltage across $$L$$ is

Accepted Answer

Across resistor, $$I = {V \over R} = {{100} \over {1000}} = 0.1A$$
At resonance,
$${X_L} = {X_C} = {1 \over {\omega C}}$$
$$ = {1 \over {200 	imes 2 	imes {{10}^{ - 6}}}} = 2500$$
Voltage across $$L$$ is
$$I{X_L} = 0.1 	imes 2500 = 250V$$

Answer

$$2.5 	imes {10^{ - 2}}V$$

Answer

$$40$$ $$V$$

Answer

$$250$$ $$V$$

Answer

$$4 	imes {10^{ - 3}}V$$

AC fundamentals

In a series resonant $LCR circuit, the voltage across R is 100 volts and R = 1\,k\Omega with C = 2\mu F. The resonant frequency \omega is 200 rad/s. At resonance the voltage across L$ is

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