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A series R-L-C circuit having R = 5 тДж, L = 400 H and C = 4F is fed from a 400 тИа 0┬░ volt supply. Then the voltage across the capacitor at resonance will be _________.
200 V
800 V
400 V
1000 V
800 V
At resonance, the inductive reactance equals the capacitive reactance, i.e., XLтАЛ=XCтАЛ. In a series RLC circuit at resonance, the circuit behaves purely resistive, and the voltage across the inductor and capacitor are equal in magnitude but opposite in phase, resulting in a voltage magnification known as the Quality Factor (Q).
At resonance, the inductive reactance equals the capacitive reactance, i.e., XLтАЛ=XCтАЛ. In a series RLC circuit at resonance, the circuit behaves purely resistive, and the voltage across the inductor and capacitor are equal in magnitude but opposite in phase, resulting in a voltage magnification known as the Quality Factor (Q).
╧Й0тАЛ=LCтАЛ1тАЛ тАФ Resonant angular frequency
Q=R1тАЛCLтАЛтАЛ тАФ Quality factor for series RLC circuit
VCтАЛ=QтЛЕV тАФ Voltage across capacitor at resonance
The resonant frequency is given by ╧Й0тАЛ=LCтАЛ1тАЛ. The Quality Factor Q is defined as R╧Й0тАЛLтАЛ=R1тАЛCLтАЛтАЛ. At resonance, the voltage across the capacitor VCтАЛ=Q├ЧVsupplyтАЛ. Using the given values, Q=51тАЛ4400тАЛтАЛ=51тАЛ100тАЛ=510тАЛ=2. Thus, VCтАЛ=2├Ч400=800┬аV.
At resonance, series RLC circuits exhibit voltage magnification across reactive components.
The voltage across the capacitor is Q times the source voltage.
The total impedance at resonance is minimum and equal to the resistance R.
Used for frequency selection in communication circuits.
Achieves high voltage gain without active components.
Can cause component insulation failure due to high voltage magnification.
Requires high precision components to maintain stable resonance.
Radio tuning circuits.
Band-pass filter design.
For this circuit, R=5╬й, L=400┬аH, C=4┬аF. Resonance occurs at ╧Й=400├Ч4тАЛ1тАЛ=401тАЛ=0.025┬аrad/s.
Option A is incorrect as it represents the source voltage without the magnification factor.
Option B is the correct result of QтЛЕVsupplyтАЛ.
B is correct тАФ The voltage across the capacitor at resonance is calculated by multiplying the source voltage by the circuit's Quality Factor (Q=2), yielding 800 V.
Always verify if the circuit is in series or parallel resonance, as the voltage magnification Q formula is applied differently for each.
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