Question

In the network shown below, the equivalent resistance between P and Q is $\frac{4}{3}\Omega$ Hence the value of r is

• A. $3\Omega$
• B. $3.6\Omega$
• C. $4\Omega$
• D. $6\Omega$

Answer 1

The correct option is D $6\Omega$

The equivalent circuits are shown.

While making equivalent circuits we have to take care that each resistor should be attached to same potential difference that is why $3\Omega$ and $r$ resistors can be shown as separate as their ends are at potential of P and Q.

Now,

$\frac{1}{R}=\frac{1}{3}+\frac{1}{4}+\frac{1}{r}$

$⟹\frac{1}{r}=\frac{3}{4}-\frac{1}{3}-\frac{1}{4}$

$⟹\frac{1}{r}=\frac{2}{12}$

$⟹r=6\Omega$

Answer-(D)