Question

In the circuit shown in figure, the
heat produced in 5 ohm
resistance is 10 calories per
second. The heat produced in 4 resistance is
​

Answer 1

Heat produced, $\large H = 1^{2} Rt$

here, $\large \frac {H_{5}}{t} = I^{2}_{5} R_{5} = 10 → I_{5} = \sqrt{ \frac{ 10 }{ 5 } } = \sqrt {2}$ . This is the current through resistor 5Ω.

Voltage across resistor 5Ω is $\large V_{5} = I_{5} R_{5} = \sqrt {2} × 5 = 5 \sqrt {2} V$

as resistors (4,6) and 5 are in parallel, so potential across (4,6) is equal to $\large V_{5}$

As resistor 4 and 6 are in series so current through each resistor $\large I_{4} = I_{6} = \frac {V_{5}}{4+6} = \frac {5 \sqrt {2}}{4+6} = \frac { \sqrt {2}}{2}$

Heat produce in resistor 4 per sec $\large I^{2}_{4} R_{4} = ( \frac { \sqrt {2}}{2})^{2} × 4 = 2cal / sec$