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Question

In the circuit shown in the figure, the current measured by the ammeter is


A

1A

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B

2A

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C

3A

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D

0

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Solution

The correct option is C

3A


Step 1: Series LCR Circuit

We know that the current in a series LCR circuit impressed by an ac emf v=V0cosωt is given by

i=I0cosωt-ϕ,

Where I0=V0R2+ωL-1ωC2 and ϕ=tan-1ωL-1ωCR

The RMS current is Ir=VrR2+ωL-1ωC2, 1

Where Vr is the RMS voltage. Thus, Ir depends on the frequency ω of the impressed ac emf.

Step 2: Phasor Diagram

The given circuit can be represented in a phasor diagram as

Step 3: Calculate the Current

From the graph we get

100-602+VR2=Vnet

402+VR2=50

402+VR2=502

VR2=2500-1600

VR2=900

VR=30

Given that R=10Ω

I=VR

=3010=3A

Hence, the correct answer is option (C).


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