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JEE Main2017PhysicsAlternating CurrentActual

A sinusoidal voltage of peak value 283 V and angular frequency 320 s - 1 is applied to a series L C R 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-

Options

  1. A10  Ω   a n d  tan - 1 ⁡ 5 3
  2. B7 Ω a n d 45 o
  3. C7 Ω a n d tan - 1 ⁡ 5 3
  4. D10 Ω a n d tan - 1 ⁡ 8 3

Correct answer

B. 7 Ω a n d 45 o

Step-by-step solution

ε 0 = 283   volt ,     ω = 320  s - 1 X L = 320 × 25 × 10 - 3 = 8   Ω X C = 1 ω C = 1 320 × 1000 × 10 - 6 X C = 10000 320 = 3.1   Ω R = 5 Ω Z =   R 2 + X L - X C 2 =   50  ≈ 7 Ω tan ⁡ ϕ = X L - X C R = 1 ⟹ ϕ = 45 o

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