Answer
We can rank the circuits according to the time taken to fully discharge the capacitors during the oscillations:
$(b) \gt (a) \gt (c)$
Work Step by Step
We can write an expression for the period of oscillation:
$T = \frac{2\pi}{\omega} = 2\pi~\sqrt{LC}$
The capacitor will be fully discharged at a time $\frac{T}{4}$
We can find the equivalent capacitance for each circuit:
Circuit (a):
$C_{eq} = C$
Circuit (b):
$C_{eq} = 2C$
Circuit (c):
$\frac{1}{C_{eq}} = \frac{1}{C}+\frac{1}{C} = \frac{2}{C}$
$C_{eq} = \frac{C}{2}$
Since $L$ is the same for all three circuits, the time to discharge the capacitor increases as the capacitance increases.
We can rank the circuits according to the time taken to fully discharge the capacitors during the oscillations:
$(b) \gt (a) \gt (c)$
