Percentage Error in Resistance JEE Physics Question

 

❓ Question

Given,

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

where,

$$V=(50\pm2)\,V$$

and

$$I=(20\pm0.2)\,A$$

If the percentage error in resistance $R$ is $x\%$, find $x$.

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✍️ Solution

Given,

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

For maximum fractional error,

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

Therefore, percentage error is

$$\frac{\Delta R}{R}\times100 = \left( \frac{\Delta V}{V} + \frac{\Delta I}{I} \right)\times100$$

Substituting the values,

$$x = \left( \frac{2}{50} + \frac{0.2}{20} \right)\times100$$
$$x=(0.04+0.01)\times100$$
$$x=5$$

✅ Final Answer

$$\boxed{x=5}$$

Hence, the percentage error in resistance is

$$\boxed{5\%}$$