Electromagnetic Induction and Alternating Current 4 Question 17

####17. In an LR series circuit, a V sinusoidal voltage V=V0sinωt is applied. It is given that L=35mH, R=11Ω,Vrms =220V,

ω/2π=50Hz and π=22/7. Find the amplitude of current in the steady state and obtain the phase difference between the current and the voltage. Also plot the variation of current for one cycle on the given graph.

(2004,4M)

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Answer:

Correct Answer: 17. 20A,π4

Solution:

  1. Inductive reactance,

XL=ωL=(50)(2π)(35×103)11Ω

Impedence, Z=R2+XL2=(11)2+(11)2=112Ω

Given, Vrms=220V

Hence, amplitude of voltage,

V0=2Vrms=2202V

Amplitude of current, i0=V0Z=2202112 or i0=20A

Phase difference, φ=tan1XLR=tan11111=π4

In LR circuit, voltage leads the current. Hence, instantaneous current in the circuit is

i=(20A)sin(ωtπ/4)

Corresponding it graph is shown in figure.



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