Question

In the circuit shown in figure, the 5 $\Omega$ resistance develops 20.00 cal/s due to the current flowing through it. The heat developed in 2 $\Omega$ resistance (in cal/s) is

• A. 23.8
• B. 14.2
• C. 11.9
• D. 7.1

Answer 1

The correct option is B 14.2

Let $I_1=$ current through $5\Omega$ and $I_2=$ current through combine $(6+9)\Omega$ resistance.

here, heat produced in $5\Omega$ per sec $=I_1^2{R}_5=20$

or $I_1=\sqrt{20/5}=2A$

As resistor 5 and (6+9) are in parallel, so potential across C and D is $V_{cd}=5I_1=5\times 2=10V$

thus, current $I_2=V_{cd}/(6+9)=10/15=2/3A$

hence, $I=I_1+I_2=2+2/3=8/3A$

Heat produced per sec in $2\Omega =I^2{R}_2=(8/3{)}^2\times 2=14.2$ cal