Question

A Wheatstone bridge has the resistance $10\Omega ,10\Omega ,10\Omega$ and $30\Omega$ in its four arms. What resistance joined in parallel to $30\Omega$ resistance will bring it to the balanced condition?

• A. $2\Omega$
• B. $5\Omega$
• C. $10\Omega$
• D. $15\Omega$

Answer 1

Answer: (D)

$15\Omega$

The equivalent resistance of the 30 ohm arm, after attaching a parallel resistance across it, must be 10 ohm, so that the bridge becomes balanced.

So, we have, for the attached parallel resistance $R$:

$\frac{1}{30}+\frac{1}{R}=\frac{1}{10}\Rightarrow \frac{1}{R}=\frac{1}{10}-\frac{1}{30}=\frac{1}{15}\Rightarrow R=15\Omega$