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Dear anshu ,
Total resisitance of the circuit = (R2 || R3) + R1
Req = R2 R3/R2 + R3 + R1 ; solving we get , Req = 3 Ω
Now time constant of the circuit = Req c = 18 ms
now apply the transient current equation , i = (V/Req) (e-t / Time constant)
we get , i = (10/3) ( e-t/18ms) A
now we can see that current in R2 and R3 divides equally as they are eual . so , current in R2 = i/2
Applying joule 's heat formula -
Total heat dissipated = ∫iR2 R dt = ∫ (100/9 ( e-t/18ms)2 * 2* dt = (200/9) ∫ e-2t/18ms dt ( limits from 0 to infi )
= ( 200/9) * (9 ms) = 200 mJ = 2 *106µJ
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