An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to Q 0 and then connected to the L and R as shown below: If a student plots graphs of the square of maximum charge Q M a x 2 on the capacitor with time (t) for two different values L 1 and L 2 ( L 1 L 2 ) of L then which of the following represents this graph correctly? (plots are schematic and not drawn to scale)

Question

An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to Q 0 and then connected to the L and R as shown below: If a student plots graphs of the square of maximum charge Q M a x 2 on the capacitor with time (t) for two different values L 1 and L 2 ( L 1 > L 2 ) of L then which of the following represents this graph correctly? (plots are schematic and not drawn to scale), , , ,

MARKS App · Accepted Answer

Comparing to the damped pendulum. We write, m d v d t = - kx - bv , b v is resistive force, ⇒ Amplitude, A = A 0 e - bt 2 m . Comparing results, we can write q c = + L d i d t + iR , as charge decreasing, q c = L d 2 q d t 2 - d q d t R ⇒ A = q ; R = b , m = L ⇒ q = q 0 e - Rt 2 L ⇒ q 2 = q 0 2 e - Rt L ⇒ q 2 = q 0 2 e - Rt L . Exponentially decreasing function, L 1 graph has higher values than L 2 .

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