Question

. In a series resonant RLC circuit, the
voltage across 100 ohm resistor is 40 V.
The resonant frequency w is 250 rad/s.
If the value of C is 4 uF, then the voltage
across L is​

Answer 1

Answer:

In a series resonant RLC circuit, the voltage across

resistor is 40 V. The resonant frequency

" is "250//s.

muF,

Answer 2

Answer:

Voltage through L = 400 V

Explanation:

Given:

Voltage across resistor = 40 V

Resistance of resistor = 100 Ω

Resonant frequency = 250 rad/s

Capacitance = 4 μF = 4 × 10⁻⁶ F

To Find:

Voltage across L

Solution:

First finding the inductive reactance $\sf X_L$ given by,

$\sf X_L= \omega \: L$

Since it is a resonant circuit, $\sf X_L=X_C$ where $\sf X_C$ is the capacitive reactance given by,

$\sf X_C=\dfrac{1}{\omega \:C}$

Hence,

$\sf X_L=\dfrac{1}{\omega \:C}$

Substitute the given data,

$\sf X_L=\dfrac{1}{250\times 4\times 10^{-6}}$

$\sf X_L=\dfrac{1}{ 10^{-3}}=10^3\: \Omega$

Now finding the current passing through the inductor,

By Ohm's Law we know that,

I =V/R

Substitute the data,

$\sf I=\dfrac{40}{100}$

$\sf I=0.4\:A$

Now finding the voltage through L given by,

$\sf V=X_L\times I$

Substituting the data,

$\sf V=10^3\times 0.4$

$\sf V=400\:V$

Hence the voltage through L is 400 V.