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This mock test of Test: Power In an AC Circuit for JEE helps you for every JEE entrance exam.
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QUESTION: 1

Find the total voltage applied in a series RLC circuit when i=3mA, VL=30V, VC=18V and R=1000 ohms.

Solution:

Explanation: Total voltage= VR+VL+VC.

VR=1000x3x10-3=3V.

Therefore, total voltage = 30+18+3=51V.

QUESTION: 2

The power factor of an RL circuit 1/root2. If the frequency of a.c. is doubled, what will be the power factor?

Solution:

QUESTION: 3

When an emf E = 7cos wt is applied across a circuit, the current is I = 5coswt. What is the power factor for the circuit?

Solution:

Since E and I are in the same phase.

Therefore, phase difference will be 0 and since power factor= cosx (where x= phase difference) and x =0

therefore, cos x or power factor will be =1

QUESTION: 4

What is value of power factor if Ø = 90°

Solution:

P=I_{rms} V_{rms} cos ϕ

Where, ϕ=90

cosϕ=0

therefore,P=0

hence the correct answer is option A.

QUESTION: 5

Power in an ac circuit is equal to

Solution:

QUESTION: 6

If the instantaneous current in a circuit is given by i = 2 cos (ωt - φ) A, the rms value of the current is

Solution:

i=2cost

=Imcost

So, Im=2amp

IRMS=Im/√2

=2/√2

=2amp

QUESTION: 7

Find the true power given apparent power = 10 W and power factor = 0.5

Solution:

The formula of true power is,

True power=Apparent power x power factor

So, true power=10 x 0.5

True power=5W

QUESTION: 8

What is the average power/cycle in a capacitor?

Solution:

The average power consumed/cycle in an ideal capacitor is 0.

The average power consumed in an ideal capacitor is given as based on the instantaneous power which is supplied to the capacitor:

p_{c} = iv= (i_{m} cos ωt)(v_{m} sin ωt)

p_{c} = i_{m}v_{m} (cos ωt sin ωt)

pc=(i_{m}v_{m}/2)sin2ωt

We know that sin ωt = 0

Therefore, average power = 0

QUESTION: 9

What is phase angle given R = 10, Z = 20

Solution:

Cos x (power factor) = R/Z

= 10/20

=1/2

x= 60

QUESTION: 10

In a circuit, the reactance X and resistance R are equal. What is the power factor?

Solution:

Given that,

Reactance (X) =Resistance (R)

tanϕ = X/R

So, we have ϕ = π/4

Power factor = cosϕ = 1/√2

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