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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Electromagnetic Induction

NTA Abhyas 2020 · Physics · Electromagnetic Induction

A coil of inductive reactance 3 1 Ω has a resistance of 8 Ω . It is...

A coil of inductive reactance 31Ω3 1 Ω has a resistance of 8Ω8 Ω. It is placed in series with a condenser of capacitive reactance 25Ω2 5 Ω. The combination is connected to an ac source of 110V\text{110}\text{V}. The power factor of the circuit is

Options

  1. A0.33\text{0}\text{.33}
  2. B0.56\text{0}\text{.56}
  3. C0.64\text{0}\text{.64}
  4. D0.80\text{0}\text{.80}

Correct answer

D. 0.80\text{0}\text{.80}

Step-by-step solution

XL=31Ω,XC=25Ω,R=8Ω{X}_{L} = 3 1 Ω \text{,} {X}_{C} = 2 5 Ω \text{,} \text{R} = 8 Ω

Impedance of series LCRLCR is

Z=(R2)+(XL−XC)2\text{Z} = \sqrt{\left(R^{2}\right) + {\left({X}_{L} - {X}_{C}\right)}^{2}}

=(8)2+(31−25)2=64+36=10Ω= \sqrt{{\left(8\right)}^{2} + {\left(3 1 - 2 5\right)}^{2}} = \sqrt{6 4 + 3 6} = 1 0 Ω

Power factor, \text\cos ϕ = \dfrac{\text{R}}{\text{Z}} = \dfrac{8}{1 0} = \text{0.8}
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