$[20]$Given the circuit schematic as $$shown in $$Fig$.1($a$)$and the circuit breaker trip

characteristic in Fig. $1($b$).$Consider a short$-$circuit fault downstream of the $20$A circuit breaker but upstream of the $2$A ones as $$indicated in $$Fig$.1($b$).$

$[10]($a$)$Consider the ambient temperature of$20$C$.$For a possible fault current of$60$A$,$ what is $$the range of $$possible tripping time of $$the $20$A circuit breaker?

$[8]($b$)$Assume that the possible fault current is $$between $60$A and $80$A$($the minimum fault current is$60$A and maximum fault current is$80$A$)$and the ambient temperature may vary from $-40$C$$to$57$C$.$Estimate the range of $$possible tripping time of $$the $20$A circuit breaker

$[2]($c$)$Based on $$the analysis results in$($b$),$what should the tripping time of $$the smart

contactor be $$for the fault current range and temperature variation range given in$($b$)?$

Location of assumed short circuit

Lavarsemices

Fig $1($a$)$