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Q.

In an ac circuit containing a resistor and an inductor connected in series, supply voltage (v) and resulting current are given by v = 100 sin 200t volt and i = 50 sin (200t - π/3) Amp. Then the resistance of the resistor is

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a

2Ω

b

12Ω

c

3Ω

d

1Ω

answer is D.

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Detailed Solution

Phase difference between v and i is ϕ=π3∴XLR=tan π3⇒XL=R tan 60o=3RImpedance  Z=VrmsIrms=100/250/2Ω=2ΩNow, XL2+R2=Z2⇒3R2+R2=(2)2⇒R=1Ω
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In an ac circuit containing a resistor and an inductor connected in series, supply voltage (v) and resulting current are given by v = 100 sin 200t volt and i = 50 sin (200t - π/3) Amp. Then the resistance of the resistor is