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Question:

A sinusoidal voltage of peak value 283V and angular frequency 320/s is applied to a series LCR circuit. Given that R=5Ω, L=25mH and C=1000µF. The total impedance, and phase difference between the voltage across the source and the current will respectively be:

7Ωand45o

10Ωandtan⁻¹(83)

7Ωandtan⁻¹(53)

10Ωandtan⁻¹(53)

Solution:

XC=1/ωc=1/(320100010⁻⁶)=3.125Ω
XL=ωL=3202510⁻³=8Ω
R=5Ω
Total impedance =√R²+(XC−XL)²=√5²+(8−3.125)²≈7Ω
tanφ=(XC−XL)/R → φ≈tan⁻¹(1) → φ=45⁰