Find capacitance $C$ for the given circuit.
Given: $ L = 20\text{ H}, \quad R = 100\Omega, \quad \omega = 100\text{ rad/s} $
The applied voltage and current are: \[ V = V_0 \sin \omega t, \quad i = i_0 \sin \omega t \]

Question

In an ideal step up transformer, the number of turns in primary coil and secondary coil are 100 and 200 respectively. If output current is found to be 5A, then input current will be ______.

Answer 1

To find the capacitance $ C $ in the given circuit, we need to use the concept of resonance in an RLC series circuit. At resonance, the impedance of the inductor and the capacitor cancel each other out, and the circuit behaves as a purely resistive circuit. Mathematically, this condition is expressed as:

$Z_L = Z_C$

where $Z_L$ is the inductive reactance and $Z_C$ is the capacitive reactance.

The inductive reactance $(Z_L)$ is given by:

$Z_L = \omega L$

And the capacitive reactance $(Z_C)$ is given by:

$Z_C = \frac{1}{\omega C}$

At resonance:

$\omega L = \frac{1}{\omega C}$

Rearranging the formula to solve for $ C $:

$C = \frac{1}{\omega^2 L}$

Substitute the given values:

$\omega = 100\, \text{rad/s}, \quad L = 20\, \text{H}$

$C = \frac{1}{(100)^2 \times 20}$

$C = \frac{1}{10000 \times 20}$

$C = \frac{1}{200000}$

$C = 5 \times 10^{-6}\, \text{farad}$

Thus, the correct answer is:

$5 \times 10^{-6}$ farad

Find capacitance $C$ for the given circuit.
Given: \( L = 20\text{ H}, \quad R = 100\Omega, \quad \omega = 100\text{ rad/s} \)
The applied voltage and current are: \[ V = V_0 \sin \omega t, \quad i = i_0 \sin \omega t \]

Show Hint

The Correct Option is A

Solution and Explanation

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Find capacitance $C$ for the given circuit.Given: \( L = 20\text{ H}, \quad R = 100\Omega, \quad \omega = 100\text{ rad/s} \)The applied voltage and current are: \[ V = V_0 \sin \omega t, \quad i = i_0 \sin \omega t \]