Question

The effective resistance between $p$ and $q$ in given figure is

• A. $2\Omega$
• B. $3\Omega$
• C. $5\Omega$
• D. $6\Omega$

Answer 1

Answer: (B)

Figure is equivalent to the one shown below.
It is a Wheatstone's bridge in which

$P=\frac{6\times 3}{6+3}=2\Omega$
$Q=\frac{8}{2}=4\Omega$
$R=\frac{4}{2}=2\Omega$
and $S=\frac{20\times 5}{20+5}=4\Omega$
We find that $\frac{P}{Q}=\frac{2}{4}=\frac{R}{S}$
i.e. the bridge is balanced. Effective resistance between $p$ and $q$
$R_{AB}=\frac{(P+Q)(R+S)}{P+Q+R+S}=\frac{(2+4)(2+4)}{2+4+2+4}$
$=\frac{6\times 6}{12}=3\Omega$