Question

Calculate the value of resistor $X$.

Answer 1

In the circuit, one $4\Omega$ resistor, one $12\Omega$ resistor and a $6\Omega$ resistor are in parallel.

Let the equivalent resistance of these three resistors is $R_p$

$\therefore \frac{1}{R_p}=\frac{1}{4}+\frac{1}{12}+\frac{1}{4}$

$\therefore R_p=2\Omega$

Now, the $4\Omega$, $R_p$ and $X$ are in series.

Thus, the total equivalent resistance of the circuit is $2+4+X=6+X$

From Ohn's law, $V=IR$

Given that $V=8volt$, $I=0.5A$

$\therefore 8=0.5\times (6+X)$

$\Rightarrow X=10\Omega$