Question

In the circuit shown, some potential difference is applied between A and B. The equivalent resistance between A and B is R

• A. no current flows through the $5\Omega$ resistor
• B. $R=15\Omega$
• C. $R=12.5\Omega$
• D. $R=\frac{18}{5}\Omega$

Answer 1

Answer: (A), (D)

The correct options are
A no current flows through the $5\Omega$ resistor
D $R=\frac{18}{5}\Omega$

Converting given circuit into its equivalent circuit as shown in figure. The arrangement is similar to the Wheatstone network. Ratio of resistances in both arms of bridge is same hence it is balanced and no current will flow through $5\Omega$ resistance and it can be neglected.
The equivalent resistance between A and B is
$\frac{1}{R}=\frac{1}{2+4}+\frac{1}{3+6}$
$\frac{1}{R}=\frac{1}{6}+\frac{1}{9}$
$\frac{1}{R}=\frac{15}{54}$
$R=\frac{18}{5}\Omega$