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

The resistance of the wire is calculated with Ohm’s law:

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

For a quantity that is a quotient or product of measured quantities, the percentage (or relative) error in the result is the algebraic sum of the percentage errors in the individual quantities.

Given percentage error in voltage, $$\frac{\Delta V}{V} \times 100 = 3\%$$
Given percentage error in current, $$\frac{\Delta I}{I} \times 100 = 3\%$$

Therefore, the percentage error in resistance is

$$\frac{\Delta R}{R} \times 100 = \frac{\Delta V}{V} \times 100 \;+\; \frac{\Delta I}{I} \times 100$$

$$= 3\% + 3\% = 6\%$$

Hence, the error in the calculated resistance of the wire is $$6\%$$.

Option A which is: $$6\%$$