Question

The percentage error in measuring resistance with a meter bridge can be minimized by adjusting the balancing point close to

• A. $20cm$
• B. $50cm$
• C. $80cm$
• D. $100cm$

Answer 1

The correct option is B $50cm$

$\begin{array}{c}\frac{P}{Q}=\frac{x}{100-x}\\ Q=\frac{P(100-x)}{x}\\ \text{differentiating by taking log}\\ \frac{\Delta Q}{Q}=\frac{\Delta (100-x)}{100-x}+\frac{\Delta x}{x}\\ \text{Error is always added.}\\ \frac{\Delta Q}{Q}=\frac{\Delta 100}{100-x}+\frac{\Delta x}{100-x}+\frac{\Delta x}{x}\end{array}$

$\begin{array}{cc}\frac{\Delta Q}{Q}& =\Delta x[\frac{1}{100-x}+\frac{1}{x}]\\ \frac{\Delta Q}{Q}& =\Delta x\left[\frac{100}{x(100-x)}\right]\\ \frac{\Delta Q}{Q}& \to \text{min when}x=50cm.\end{array}$