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The graph shows the variation of current I with the frequency ω in an LCR circuit. What is the bandwidth?
Question

The graph shows the variation of current I with the frequency ω in an LCR circuit. What is the bandwidth?

A.

4 rad s⁻¹

B.

0.6 rad s⁻¹

C.

1.2 rad s⁻¹

D.

0.4 rad s⁻¹​

Correct option is C

Correct answer is C
Explanation
We know that the bandwidth is given by:
Bandwidth = (ω2 - ω1)
Here, ω1 and ω2 are the two angular frequencies at which the current amplitude of the LCR circuit becomes Imax / √2. At this point, the current is 0.707 times its maximum value, and the current reaches its peak at the resonant frequency.
The RMS value of current can be expressed as:
I = E0 / √2 = 1 / √2 = 0.707 A
From the graph, the frequencies corresponding to 0.707 A current are:
ω1 = 0.8 rad/s    and    ω2 = 1.2 rad/s
Therefore, the bandwidth can be calculated as:
Bandwidth = ω2 - ω1 => 1.2 - 0.8 = 0.4 rad/s
Hence, the bandwidth of the given LCR circuit is 0.4 rad/s.

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