Alternating Current MCQs for NEET — Physics Questions with Answers

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An alternating current is given by the equation i=i1cosω t+i2sinω t. The r.m.s. current is given by

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Explanation

irms=i12+i222=12i12+i221/2 

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In an ac circuit, the current is given by i=5sin 100 t−π2 and the ac potential is V = 200 sin(100t) volt. Then the power consumption is :

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Explanation

P=Vicosϕ 

Phase difference ϕ=π2⇒P=zero  

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A resistance of 20 ohms is connected to a source of an alternating potential V=220sin(100πt). The time taken by the current to change from its peak value to r.m.s value is 

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Explanation

Peak value to r.m.s. value means current becomes 12 times.

 

Time taken by the current to reach its peak value:i=i0sin100πt⇒i0=i0sin100πt1⇒sin100πt1=sinπ2⇒t1=1200secTime taken by the current to become i2 after reaching its peak value:i=i0sin100πt⇒12×i0=i0sin100πt2⇒sin100πt2=sin3π4⇒t2=3400secTime taken by the current to change from its peak value to r.m.s. value:t2-t1=3400-1200=1400sec=2.5×10−3sec. 

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Voltage and current in an ac circuit are given by V=5sin 100πt−π6 and I=4sin 100πt+π6 

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Explanation

Phase difference Δϕ=ϕ2−ϕ=π6−−π6=π3  

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An alternating current of frequency ‘f’ is flowing in a circuit containing a resistance R and a choke L in series. The impedance of this circuit is 

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Explanation

Z=R2+XL2,  XL=ωL and ω=2πf

∴Z=R2+4π2f2L2 

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A resistance of 300 Ω and an inductance of 1π henry are connected in series to a ac voltage of 20 volts and 200 Hz frequency. The phase angle between the voltage and current is :

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Explanation

Phase angle tanϕ=ωLR=2π×200300×1π=43

∴ ϕ=tan−143

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In a LCR circuit having L = 8.0 henry, C = 0.5 μF and R = 100 ohm in series. The resonance frequency in radian per second is 

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Explanation

Resonance frequency in radian/second is

ω=1LC=18×0.5×10−6=500  rad/sec 

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The impedance of a circuit consists of 3 ohm resistance and 4 ohm reactance. The power factor of the circuit is :

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Explanation

Z=R2+X2=42+32=5 

∴  cosϕ=RZ=35=0.6 

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The power factor of a good choke coil is:

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Explanation

cosϕ=RZ.

In choke coil ϕ≈90°

So cosϕ≈0

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L, C and R represent physical quantities inductance, capacitance and resistance respectively. The combination representing dimension of frequency is 

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Explanation

Frequency =12πLC

So the combination which represents dimension of frequency is 1LC=(LC)−1/2

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