We have to calculate time that would elapse in units of time constant in a RC circuit for the capacitor to get charged within 1.00% of its equilibrium charge.

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Let be the equilibrium charge. The equation for the charging of a capacitor is

where is the time constant of the RC circuit.

If the capacitor is to be charged to within 1.00% of its equilibrium charge,

We, therefore, have

Taking the natural logarithm, i.e. with respect to base , we have