Find the total current that passes through the circuit. Find the heat generated across the each resistor.

First we need to find the total current (I) flowing in the circuit, that we can find by using Ohm’s law, because we are given with the battery’s potential difference (V) and we need to find the net resistance of the circuit (R).

As we can see there are 3 resistors 4 ohm, 6 ohm and 12 ohm, and there are two resistors in parallel the 6 and 12 ohm ones, sowe will first solve the parallel ones and get the parallel resistance R_p

R_p = 4 ohm

Now the net resistance will come by simply adding the R_p = 4 ohm and the other 4 ohm resistor because they both are now in series,

So,

R = R_p + 4 = 4 + 4 = 8 ohm

R = 8 ohm

By using Ohm’s law, V = I× R,

Now we need to find the heat generated across each resistor, which we will do by using Joule’s law of heating,

Mathematically,

Where I is current passing through conductor; T is time; R is resistance of the conductor; and H is heat generated across the conductor.

As the 4 ohm resistor is alone and in series so current I₁ passing through it will be equal to the total current passing through the circuit ,

Which is 2 A and the potential difference across the 4 ohm resistor is

V = I× R = 2× 4 = 8 V

Now the two resistors 6 and 12 ohm are in parallel that is they have same potential difference across them which is 8 V because the battery has total potential difference of 16 V and 8 V is consumed by the 4 ohm resistor which is in series and alone so , 16-8 = 8 V the remaining potential difference is 8 V which is consumed by both 6 and 12 ohm resistors in parallel.

Let the current passing through 6-ohm resistor be I₂ and current passing through 12 ohm resistor be I₃ .

By Ohm’s law,

V = I₂× R₂,

V = I₃× R₃ ,

Heat generated by 4-ohm resistor,

Heat generated by 6-ohm resistor,

Heat generated by 12-ohm resistor,

Time will be same for all the resistors always, in this case as no time is given so we will calculate for one second of heat generated or we can leave the answer in terms of T.