Question

Seven resistances are connected as shown in the given figure. The equivalent resistance between $A$ and $B$ is

• A. $3\Omega$
• B. $4\Omega$
• C. $4.5\Omega$
• D. $15\Omega$

Answer 1

Answer: (B)

Equivalent resistance of $R_1$ and $R_2$ (in parallel)

$R^{\prime }=\frac{6\times 6}{6+6}=3\Omega$
Equivalent resistance of $R_5$ and $R_7$ (in parallel)
$R^{\prime \prime }=\frac{10\times 10}{10+10}=5\Omega$
Now, the circuit is reduced to

Now, this circuit can be shown as it is balanced
$\left(\frac{5}{3}=\frac{5}{3}\right)$

Total resistance between $AB$
$R_{AB}=\frac{(5+3)(5+3)}{(5+3)+(5+3)}$
$=\frac{8\times 8}{8+8}=4\Omega$