Question

A condenser of \[250\mu F\] is connected in parallel to a coil of inductance \[0.16mH\] while its effective resistance is \[20\Omega \]. Determine the resonant frequency
(A) \[9 \times {10^4}Hz\]
(B) \[16 \times {10^7}Hz\]
(C) \[8 \times {10^5}Hz\]
(D) \[9 \times {10^3}Hz\]

Answer 1

Hint: Resonance is the phenomenon in the electrical circuit, where the output of the circuit is maximum at one particular frequency. And that frequency is known as the resonant frequency. At the thunderous recurrence, the capacitive reactance and inductive reactance are equal.An RLC circuit is an electrical circuit consisting of a resistor, an inductor, and a capacitor, associated in arrangement or in equal.

Complete step by step solution
Here \[C = 250 \times {10^{ - 6}}F\]
\[L = 0.16 \times {10^{ - 3}}H\]
\[R = 20\Omega \]
Here $c$is the capacitance $L$is the inductance and $R$is the resistance
Now the Resonant frequency of \[L,C,R\] circuit is
\[{v_0} = \dfrac{1}{{2\pi }}\sqrt {\dfrac{1}{C} - \dfrac{{{R^2}}}{{{L^2}}}} \]
Now we have to substitute the values of \[L,C,R\]in the above equation
\[{v_0} = \dfrac{1}{{2 \times 3.14}}\sqrt {\dfrac{1}{{(250 \times {{10}^{ - 6}})(0.16 \times {{10}^{ - 3}})}} - \dfrac{{20 \times 20}}{{{{(0.16 \times {{10}^{ - 3}})}^2}}}} \]
After calculating the above equation we get
\[{v_0} \cong 8 \times {10^5}Hz\]

Hence the correct answer is option (C)

Note:
A capacitor is an electrical device consisting of two conducting plates separated by an electrical insulator (the dielectric), designed to hold an electric charge. Energize fabricates when a voltage is applied over the plates, making an electric field between them.Current can move through a capacitor just as the voltage across it is changing, not when it is constant.Capacitors are utilized in power supplies, intensifiers, signal processors, oscillators, and rationale gates.An inductor is a latent part that is utilized in most force electronic circuits to store energy as attractive energy when power is applied to it. One of the key properties of an inductor is that it impedes or opposes any change in the amount of current flowing through it.
A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active elements, and terminate transmission lines, among other uses.