In a short$-$circuit test on a $3$ pole, $132$ kV circuit breaker, power factor of fault was $0\mathrm{.}3,$ armature reaction effect caused recovery voltage to be $0\mathrm{.}9$ times the full line value. The breaking current had $8\%$ asymmetry. Natural frequency of oscillations of restriking voltage was $15,000$ cycles$/$second$.$ The neutral was isolated and the fault involved earth. Calculate the following: $($a$)$ Average RRRV and maximum RRRV$.($b$)$ Time at which the restriking voltage is maximum. $($c$)$ Value of restriking voltage when t $=20$ ms