Question 457: AC fundamentals

Question

A series LCR circuit with inductance 10 H, capacitance 10 $$\mu$$F, resistance 50 $$\Omega$$ is connected to an ac source of voltage, V = 200sin(100t) volt. If the resonant frequency of the LCR circuit is v0 and the frequency of the ac source is v, then

Accepted Answer

$$\omega L = {1 \over {\omega C}}$$
$$\omega  = {1 \over {\sqrt {LC} }} = {1 \over {\sqrt {10 	imes 10 	imes {{10}^{ - 6}}} }}$$
$$\omega  = 100$$
$$\omega  = 2\pi f \Rightarrow f = {\omega  \over {2\pi }}$$
$${v_0} = {f_0} = {{100} \over {2\pi }} = {{50} \over \pi }$$ Hz, $$\omega  = 100$$
$$v = f = {{100} \over {2\pi }} = {{50} \over \pi }$$

Answer

$${v_0} = v = 50$$ Hz

Answer

$${v_0} = v = {{50} \over \pi }$$ Hz

Answer

$${v_0} = {{50} \over \pi }$$ Hz, $$v = 50$$ Hz

Answer

$$v = 100$$ Hz, $${v_0} = {{100} \over \pi }$$ Hz

AC fundamentals

A series LCR circuit with inductance 10 H, capacitance 10 $\muF, resistance 50 \Omega$ is connected to an ac source of voltage, V = 200sin(100t) volt. If the resonant frequency of the LCR circuit is v0 and the frequency of the ac source is v, then

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