Question 285: AC fundamentals

Question

In series LCR resonant circuit, R $=800 \Omega$, $\mathrm{C}=2 \mu \mathrm{~F}$ and voltage across resistance is 200 V . The angular frequency is $250 \mathrm{rad} / \mathrm{s}$. At resonance, the voltage across the inductance is

Accepted Answer

$$ \begin{aligned} &	ext { At resonance in series LCR circuit, }\ &\begin{aligned} & X_L=X_C \ & \omega L=\frac{1}{\omega C} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...(i)\ & I=\frac{V_R}{R} \end{aligned} \end{aligned} $$
Now, voltage across inductor is
$\mathrm{V}_{\mathrm{L}}=\mathrm{I} \mathrm{X}_{\mathrm{L}}$
$V_L=\frac{V_R}{R} 	imes X_L$
$\mathrm{V}_{\mathrm{L}}=\frac{\mathrm{V}_{\mathrm{R}}}{\mathrm{R}} 	imes \omega \mathrm{L}$
$\mathrm{V}_{\mathrm{L}}=\frac{\mathrm{V}_{\mathrm{R}}}{\mathrm{R}} 	imes \frac{1}{\omega \mathrm{C}}\,\,\,\,\,Ã¢ÂÂ¦.[From (i)]$
$\mathrm{V}_{\mathrm{L}}=\frac{200}{800} 	imes \frac{1}{250 	imes 2 	imes 10^{-6}}=500 \mathrm{~V}$

Answer

400 V

Answer

250 V

Answer

1000 V

Answer

500 V

AC fundamentals

In series LCR resonant circuit, R =800 \Omega, \mathrm{C}=2 \mu \mathrm{~F} and voltage across resistance is 200 V . The angular frequency is 250 \mathrm{rad} / \mathrm{s}. At resonance, the voltage across the inductance is

Choose the correct answer: