Question

The resistance of a metal is given by $R=V/I$, where $V$ is potential difference and $I$ is the current. In a circuit, the potential difference across resistance is $V=(8\pm 0.5)V$ and current in resistance, $I=(4\pm 0.2)\mathring{A}$. What is the value of resistance with its percentage error?

• A. $(2\pm 5.6\%)$
• B. $(2\pm 0.7\%)$
• C. $(2\pm 35\%)$
• D. $(2\pm 11.25\%)$

Answer 1

Answer: (D)

$(2\pm 11.25\%)$

Resistance, $R=\frac{V}{I}$ $V=(8\pm 0.5)V$

$I=(4\pm 0.2)A$

$R=\frac{V}{I}=\frac{8}{4}=2\Omega$

We know from rules of error propagation.

$\frac{\Delta R}{R}=\frac{\Delta V}{V}+\frac{\Delta I}{I}$

$=\frac{0.5}{8}+\frac{0.2}{4}=0.1125$

$\therefore$ % error $=11.25$%

$\Rightarrow$ $R=(2\pm 11.25)$%