Question

Each resistance in the given network has the value of $10\Omega$ . The equivalent resistance between points, $A$ and $B$ will be :

• A. $30\Omega$
• B. $10\Omega$
• C. $20\Omega$
• D. $2\Omega$

Answer 1

Answer: (B)

The give circuit is a balanced Wheatstone's bridge.
In the given circuit, ratio of resistances in the opposite arms is same, hence bridge is a balance one, hence diagonal resistance of $10\Omega$ will be in effective. The circuit now reduces to
$R_1=10\Omega +10\Omega =20\Omega$
$R_2=10\Omega +10\Omega =20\Omega$


$\therefore$ Effective resistance is
$\frac{1}{R^{\prime }}=\frac{1}{20}+\frac{1}{20}$
$\frac{1}{R^{\prime }}=\frac{40}{20\times 20}=\frac{1}{10}$
$R^{\prime \prime }=10\Omega$