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In the circuit shown, the frequency of the sinusoidal source is about
- a)100 Hz
- b)25 Hz
- c)50 Hz
- d)16 Hz
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In the circuit shown, the frequency of the sinusoidal source is abouta...
Concept:
Series resonance:
- The state of an electrical network at which reactance of the circuit will be zero means at fixed frequency L and C elements will exchange energy freely as a function of time, which results in sinusoidal oscillations across either inductor or capacitor.
- At resonance inductive reactance is equal to capacitive reactance, so the circuit is purely resistive in nature under series resonance.
- As the circuit is purely resistive at resonance condition. The power factor of the series RLC circuit is unity, hence the current flowing through the circuit is in phase with supply voltage.
- At resonance series, the RLC circuit offers minimum impedance which is equal to resistance only. It allows maximum current at resonance condition so it is called an acceptor circuit.
Calculation:
Given that
Resistance = R ohm
Inductance L = 0.1 H
Inductive reactance XL = ωL
Where ω is the angular frequency in rad/sec
Capacitive reactance Xc = 1 / ωC = 10 ohm
Supply voltage V = 100∠300
Current through the circuit is I = 10∠300
From the values of voltage and current we can observe that supply voltage V and current I are in phase. That means the circuit is under resonance.
At resonance XL = XC
⇒ ω L = Xc
⇒ ω × 0.1 = 10
ω = 100 rad/sec
2π f = 100
f = 100/2π = 15.92 Hz
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In the circuit shown, the frequency of the sinusoidal source is abouta)100 Hzb)25 Hzc)50 Hzd)16 HzCorrect answer is option 'D'. Can you explain this answer?
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