Question

Five resistances are connected as shown in figure. The effective resistance between the points $A$ and $B$ is

• A. $\frac{10}{3}\Omega$
• B. $\frac{20}{3}\Omega$
• C. $15\Omega$
• D. $6\Omega$

Answer 1

The correct option is A $\frac{10}{3}\Omega$

In the given circuit,the arrangement of resistances is a form of Wheatstone's bridge. Hence no current will flow through $7\Omega$ resistor. The resistances between A and B will be parallel combination of each other.
Hence,
$\frac{1}{R_{eq}}=\frac{1}{2+3}+\frac{1}{4+6}$
$\frac{1}{R_{eq}}=\frac{1}{5}+\frac{1}{10}$
$\therefore R_{eq}=\frac{5\times 10}{15}$
$\therefore R_{eq}=\frac{10}{3}\Omega$