We have to find the resistance R that should be connected to an inductor and capacitor in series in order that the maximum charge on the capacitor decays to 99% of its initial value in 50 cycles.

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In a LCR circuit the variation of charge as a function of time is given by the function

in which

.

The inductance in the circuit is

,

and the capacitance in the circuit is

.

Therefore, the period of LC-oscillations will be

We want to fix the resistance in the LCR-circuit in order that the maximum charge on the capacitor decays to 99% of its initial value in 50 cycles, that is in

We have the condition