A sinusoidal voltage of peak value 283   V and angular frequency 320   s - 1 is applied to a…

A sinusoidal voltage of peak value 283 V and angular frequency 320 s-1 is applied to a series LCR circuit. Given that R=5 Ω, L=25 mH and C=1000 μF. The total impedance and phase difference between the voltage across the source and the current will respectively be-
  1. 10 Ω and tan-1⁡53
  2. 7 Ω and 45o
  3. 7 Ω and tan-1⁡53
  4. 10 Ω and tan-1⁡83

Solution

ε0=283 volt,  ω=320 s-1

XL=320×25×10-3=8 Ω

XC=1ωC=1320×1000×10-6

XC=10000320=3.1 Ω

R=5Ω

Z= R2+XL-XC2= 50 ≈ 7Ω

tan⁡ϕ=XL-XCR=1

⟹ϕ=45o

Asked in: JEE Main 2017 (09 Apr Online)

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