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GATE 2015 EE – Question 40

Electrical and Electronic Measurements · Bridges and Potentiometers · 2 marks · Multiple choice

An unbalanced DC Wheatstone bridge is shown in the figure. At what value of $p$ will the magnitude of $V_0$ be maximum?

A Wheatstone bridge with arms $pR$ and $R(1 + x)$ on top and $pR$ and $R$ on the bottom, driven by a battery E. The output $V_0$ is taken across the middle.
  1. $\sqrt{(1 + x)}$
  2. $(1 + x)$
  3. $1/\sqrt{(1 + x)}$
  4. $\sqrt{(1 - x)}$

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Correct answer: (A) $\sqrt{(1 + x)}$

Explanation

The output is $V_0 = E\left[\frac{1 + x}{1 + x + p} - \frac{1}{1 + p}\right] = E\,\frac{p x}{(1 + p)(1 + x + p)}$. Setting the derivative with respect to $p$ to zero gives $(1 + p)(1 + x + p) - p(2 + x + 2p) = 0$, which simplifies to $1 + x - p^2 = 0$. So $p = \sqrt{1 + x}$.