A Sinusoidal Voltage of Peak Value

Answer: B. 5 Ohm

A sinusoidal voltage of peak value 283V and frequency 50Hz is applied to a series LCR circuit in which R=3Ω, L=25.48mH, and C=786μF. The impedance of the circuit is 5 ohms.

Solution:

Given that, frequency = 50 Hz

⟹ω=2πf=2π×50=100 π

Resistance (R)=  3 ohms

Inductance (L)= 25.48 mH

⟹ Inductive reactance XL=ωL=100 π(25.48×10^-3)=8 ohms 

Capacitance = 786 μF

⟹Capacitive reactance (X_c)=1/ωC=1/100π(786×10^-6)= 4 Ohms

Therefore impedance (Z) of the series LCR circuit is

Z=√(R²+(X_L–X_C)²)

⟹Z=√(3²+(8-4)²)= 5 Ohms

Hence option B is correct.

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