Question

In the circuit shown in figure, the power dissipated in the form of heat through the $6\Omega$ resistor is $6\text{W}$. What is the value of resistance $R$ in the circuit?

• A. $6\Omega$
• B. $10\Omega$
• C. $13\Omega$
• D. $24\Omega$

Answer 1

The correct option is D $24\Omega$

Given, the power dissipated through $6\Omega$ resistor $=6\text{W}$
$P=i^{2}R$

$6=i^2\times 6\Rightarrow i=1\text{A}$

$\frac{V}{R_{eq}}=1\Rightarrow \frac{12}{R_{eq}}=1\Rightarrow R_{eq}=12\Omega$

Now, $R_{eq}=6+\frac{8R}{8+R}=12$

$\Rightarrow \frac{8R}{8+R}=6$

$\Rightarrow 8R=48+6R$
$2R=48\Rightarrow R=24\Omega$

Hence, option $\left(d\right)$ is the correct answer.

Why this Question? Tip: Always remember, a resistor is a dissipative element. It dissipates power in the form of heat, and the power dissipated is given by: $P=i^{2}R$