Question

Four resistors $A, B, C$ and $D$ form a Wheatstone bridge as shown in the figure. The bridge is balanced when $C=100 \,\Omega$. If $A$ and $B$ are interchanged, the bridge balances for $C=121 \,\Omega$. The value of $D$ is

• A. $10 \,\Omega$
• B. $100 \,\Omega$
• C. $110\, \Omega$
• D. $120 \,\Omega$

Answer 1

Answer: (C)

According to the question, balanced wheat stone bridge, can be shows as follows

First case when, $C=100 \,\Omega$
Now, By balanced wheat stone bridge,
$\frac{R_{A}}{R_{B}}=\frac{100}{R}\,\,\,...(i)$
Second case when, $C=121 \,\Omega$
$\frac{R_{B}}{R_{A}}=\frac{121}{R}\,\,\,...(ii)$
From Eqs. (i) and (ii), we get
$\therefore R=\sqrt{100 \times 121}$
$R=110 \,\Omega$