Question

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

Answer 1

Given power consumed by $6\Omega$ resistor is $6\text{W}$
$P=6=i^{2}R\Rightarrow 6=i^2\times 6\Rightarrow i=1\text{Amp}$

As resistors of resistances $R$ and $8\Omega$ are in parallel
Effective resistance of them is $\frac{8R}{8+R}$

Now resistor $6\Omega$ is connected in series with combination of resistances $R$ and $8\Omega$.
$R_{\text{eq}}=(6+\frac{8R}{8+R})$

Using Ohms law
$V=i\times R_{\text{eq}}$
$12=1(6+\frac{8R}{8+R})$
$8R=6(8+R)$
$2R=48\Rightarrow R=24\Omega$