Question

In the Wheatstone bridge shown below the galvanometer G has a current sensitivity of $1\mu A/mm,$ a resistance of $2.5k\Omega$ and a scale resolution of 1 mm. Let $\Delta R$ be the minimum increase in R from its nominal value of $2k\Omega$ that can be detected by this bridge.

The value of $\Delta R$ is approximately

• A. $2.8\Omega$
• B. $3.4\Omega$
• C. $5.2\Omega$
• D. $12\Omega$

Answer 1

The correct option is B $3.4\Omega$

Writing KVL in inner loop we get,

$3\times {10}^3+0.0025-6\times {10}^3{I}_2=0$

$3\times {10}^{3}I=-0.0025+8.9976$

I = 2.9983 mA

Writing KVL in another inner loop we get,

$(R+\Delta R)\times (I-I_1)-0.0025-6.0024=0$

$(R+\Delta R)=\frac{6.0049}{(2.9983-0.001)\times {10}^{-3}}$

$R+\Delta R=2003.436$

$\Delta R=3.436\Omega$