Question

A series LCR circuit contains a pure inductor of inductance 5.0 H,
a capacitor of capacitance 20uF and a resistor of resistance 4ohm.
a) Find the resonant frequency of the circuit.
b) Calculate the Quality factor (Q-factor) of the circuit
c) What is the impedance at resonant condition?​

Answer 1

Answer:

Part a)

Resonance frequency of series LCR circuit is given as

$f = 15.91 Hz$

Part b)

Q factor is given as

$Q = 125$

Part c)

At resonance condition the impedance is same as the total resistance of the circuit

$z = 4 ohm$

Explanation:

Part a)

As we know that resonance frequency is given as

$f = \frac{1}{2\pi\sqrt{LC}}$

So we have

$f = \frac{1}{2\pi\sqrt{5\times 20 \times 10^{-6}}}$

$f = 15.91 Hz$

Part b)

Now we know that Q factor is given as

$Q = \frac{1}{R}\sqrt{\frac{L}{C}}$

$Q = \frac{1}{4}\sqrt{\frac{5}{20\times 10^{-6}}}$

$Q = 125$

Part c)

At resonance condition the impedance is same as the total resistance of the circuit

So we have

$z = R$

$z = 4 ohm$

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Topic : resonance LCR circuit

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