Q74 / 90 · JEE Main 2012 (Offline) · Physics

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are $3 \%$ each, then error in the value of resistance of the wire is

  • Correct answer
    A
    $6 \%$
  • B
    zero
  • C
    $1 \%$
  • D
    $3 \%$

Solution

$\mathrm{R}=\frac{\mathrm{V}}{\mathrm{i}}$ $\Rightarrow \quad\left|\frac{\Delta \mathrm{R}}{\mathrm{R}}\right|=\left|\frac{\Delta \mathrm{V}}{\mathrm{V}}\right|+\left|\frac{\Delta \mathrm{i}}{\mathrm{i}}\right|$ $\frac{\Delta \mathrm{V}}{\mathrm{V}} \times 100=3$ $\Rightarrow \quad \frac{\Delta \mathrm{V}}{\mathrm{V}}=0.03$ Similarly, $\frac{\Delta i}{i}=0.03$ Hence $\frac{\Delta \mathrm{R}}{\mathrm{R}}=0.06$ So percentage error is $\frac{\Delta \mathrm{R}}{\mathrm{R}} \times 100=6 \%$

Hence, the correct answer is option: 'A'.

Relevant Questions