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, $I=(4 \pm 0.2) A$. What is the value of resistance with its percentage error?

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

Answer 1

Answer: (D)

$R=\frac{V}{I}=\frac{8}{4}=2 \Omega$
$\frac{\Delta R}{R} \times 100=\frac{\Delta V}{V} \times 100+\frac{\Delta I}{I} \times 100$
$=\frac{0.5}{8} \times 100+\frac{0.2}{4} \times 100=11.25 \%$
$\Rightarrow R=(2 \pm 11.25 \%) \Omega$