SHMHard
Question
An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to Q0 and then connected to the L and R as shown below :-
If a student plots graphs of the square of maximum charge 2 Max (Q ) on the capacitor with time (t) for two different values L1 and L2 (L1 > L2) of L then which of the following represents this graph correctly ? (plots are schematic and not drawn to scale)
If a student plots graphs of the square of maximum charge 2 Max (Q ) on the capacitor with time (t) for two different values L1 and L2 (L1 > L2) of L then which of the following represents this graph correctly ? (plots are schematic and not drawn to scale)
Options
A.
B.
C.
D.
Solution
As damping is happening its amplitude would vary as
The oscillations decay exponentially and will be proportional to e-γt where γ depends inversely on L.
So as inductance increases decay becomes slower
∴ for
The oscillations decay exponentially and will be proportional to e-γt where γ depends inversely on L.
So as inductance increases decay becomes slower
∴ for
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