Question

If voltage $V=\left(100\pm 5\right)V$ and current $I=\left(10\pm 0.2\right)A$, the percentage error in resistance $R$ is:

• A. $5.2\%$
• B. $25\%$
• C. $7\%$
• D. $10\%$

Answer 1

The correct option is C

$7\%$

Step 1: Given

Voltage: $V=100V$

Error in voltage: $∆V=\pm 5V$

Current: $I=10A$

Error in current: $∆I=\pm 0.2A$

Step 2: Formula Used

$R=\frac{V}{I}$, Where $R$ is the resistance.

Error Correction Formula: $\frac{∆R}{R}\times 100=\frac{∆V}{V}\times 100+\frac{∆I}{I}\times 100$,

Where $∆R$ is the error in resistance.

Step 3: Calculate the error in resistance

$\begin{array}{rcl}\frac{∆R}{R}\times 100\%& =& \frac{\pm 5}{100}\times 100\%+\frac{\pm 0.2}{10}\times 100\%\\ & =& \pm \left(\frac{5}{100}+\frac{2}{100}\right)\times 100\%\\ & =& \pm \left(\frac{5+2}{100}\right)\times 100\%\\ & =& \pm 7\%\end{array}$

Hence, the percentage error in resistance is $\begin{array}{rcl}& & \pm 7\%\end{array}$.