Alternating Current

JEE Main level, single correct, medium

138 of 190

Question 138 of 190

A sinusoidal voltage of peak value 283V283V and angular frequency 320s−1320{s}^{-1} is applied to a series LCRLCR circuit. Given that R=5Ω,L=25mHR=5\Omega ,L=25mH and C=1000μFC=1000\mu F. The total impedance and phase difference between the voltage across the source and the current will respectively be-

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Answer: (B) 7Ωand45o7\Omega and{45}^{o}

ϵ0=283volt,ω=320s−1{\epsilon }_{0}=283volt,\omega =320{s}^{-1}

XL=320×25×10−3=8Ω{X}_{L}=320\times 25\times {10}^{-3}=8\Omega

XC=1ωC=1320×1000×10−6{X}_{C}=\dfrac{1}{\omega C}=\dfrac{1}{320\times 1000\times {10}^{-6}}

XC=10000320=3.1Ω{X}_{C}=\dfrac{10000}{320}=3.1\Omega

R=5ΩR=5\Omega

Z=R2+(XL−XC)2=50≈7ΩZ=\sqrt{{R}^{2}+{\left({X}_{L}-{X}_{C}\right)}^{2}}=\sqrt{50}\approx 7\Omega

tan⁡⁡ϕ=XL−XCR=1\tan ⁡\phi =\dfrac{{X}_{L}-{X}_{C}}{R}=1

⟹ϕ=45o⟹\phi ={45}^{o}

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