  # A Sinusoidal Voltage of Peak Value

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Updated on: September 25th, 2023 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. What is the impedance of the circuit?
A. 3 ohms
B. 5 ohms
C. 7.5 ohms
D. 9 ohms

## 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 (Xc)=1/ωC=1/100π(786×10-6)= 4 Ohms

Therefore impedance (Z) of the series LCR circuit is

Z=√(R2+(XLXC)2)

⟹Z=√(32+(8-4)2)= 5 Ohms

Hence option B is correct.

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