Problem 175 - A Complete Resource Book in Physics for JEE Main

Question

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 (A) \(6 \%\) (B) Zero (C) \(1 \%\) (D) \(3 \%\)

Step-by-Step Solution

Answer

The error in the value of resistance of the wire is \(6\%\). The correct answer is (A) \(6\%\).

Step 1: Write Ohm's Law formula

The relationship between voltage (V), current (I), and resistance (R) is given by Ohm's Law: \[ V = I R \]

Step 2: Rearrange to find the resistance formula

In order to find the resistance, rearrange the formula as: \[R=\frac{V}{I}\]

Step 3: Calculate the percentage error in resistance

The percentage error in a product or a quotient (in our case, a quotient) is equal to the sum of the percentage errors of all the variables. In this scenario, the percentage error in the measurement of current and voltage is \(3 \%\) each. Therefore, percentage error in R = percentage error in V + percentage error in I \[ \% R = \% V + \% I\]

Step 4: Substitute the values and find the percentage error in resistance

Given the percentage error in the measurement of current and voltage, we plug the values into the formula we established in Step 3: \[\% R = 3\% + 3\%\] \[\% R = 6\%\] So, the error in the value of resistance of the wire is \(6\%\).\ The correct answer is: (A) \(6\%\).