i have putted the right answer but i dont know how did he got it explain plz In

Question

i have putted the right answer but i dont know how did he got it explain plz

In the above complex circuit, the constant perfect battery has been connected for a large period of time so that the currents all have steady values. Given these facts, calculate each of the following: At some later time, the connection at point P breaks, causing the current in the 9-ohm resistor to becomes zero. Calculate the total amount of heat energy dissipated in the 8-ohm resistor after the connection fails. 250 mu J

Explanation / Answer

after long time, no current will pass throught the capacitor.

so 8 ohm and 4 ohm will be in series. then equivalent of these two will be in parallel with middle 4 ohm.

8 ohm and 4 ohm in series.

R = 8 + 4 = 12 ohm

R and 4ohm in parallel,

1/R' = 1/12 + 1/4

R' = 3 ohm

now R' and 9ohm in series with battery.

Req = 3 + 9 = 12 ohm

current throught battery, I = 120/12 = 10 A

curren throught R , I' = I x 4 / (4 + R) = 10 x 4 / (4 + 12) = 2.5 A

PD across capacitor, Vc = 4 I' = 4 x 2.5 = 10 Volt.

so total stored energy in capacitor,

U = C V^2 /2 = (30 x 10^-6) x 10^2 / 2 = 1.5 x 10^-3 J

after disconnected.

current will flow in 4ohm, 8ohm and then middle 4ohm.

now middle 4ohm and 8 ohm will be in series. say equivalent is r.

then r, 4ohm and capacitor will be in parallel connection.

now energy will flow from capacitor to 4ohm and r.

so branch having less resistance, more energy will be dissipated and in ratio of resistances.

U1 + U2 = 0.0015

and U1 / U2 = (4) / (12)

U2 = 3 U1

U1 + 3U1 = 0.0015

U1 = 0.000375 J

this is the energy dissipated throught branch r.

in this branch, 4 and 8 ohm are in series.

so energy will divided in the ratio of resistance.

{more resistance, more energy}

U8 / U4 = 8 / 4 = 2

U4 = 0.5 U8

and U4 + U8 = U1 = 0.000375

0.5U8 + U8 = 0.000375

U8 = 2.5 x 10^-4 J Or 250 x 10^-6 J Or 250 uJ

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