The figure shows current varying with time. The magnitude of constant direct current for a particular time which would produce same heat in an identical resistance as produced by given time varying current in three seconds.

Heat =∫​i2Rdt​=∫01(t)2Rdt+∫1212Rdt+∫23(3−t)2Rdt=13R+R+R3=5R3​∵equation of straight first line= y=mx+ c⇒i=1(t)+0=t; equation of straight  second line= y=mx+ c⇒i=0(t)+(-1)=-1;equation of straight third line= y=mx+ c⇒i=-1(t)+C; 0=(-1)3 +C; C=3∴ i=-1t+3Case 1 : I12R×3=5R3⇒I12=59⇒I1=53A​Case 2 : I22R×15=5R3⇒I2=13A