Question

The potential difference across the ends of a conductor is $ (50 \pm 3) $ V and the current through it is $ (5 \pm 0.1) $ A. The percentage error in the measurement of the resistance of the conductor is: Options:

• A. \( 2 \)
• B. \( 4 \)
• C. \( 8 \)
• D. \( 6 \)

Hint:

When calculating the error in a quotient like \( R = \frac{V}{I} \), the relative errors of the numerator and denominator add up in magnitude.

Answer 1

The Correct Option is C

We are given the potential difference \( V = (50 \pm 3) \) V and the current \( I = (5 \pm 0.1) \) A. We need to find the percentage error in the resistance \( R \). Step 1: Determine the resistance and its uncertainty.
The resistance \( R \) is given by Ohm’s Law: \[ R = \frac{V}{I} \] Nominal values: \( V = 50 \) V, \( I = 5 \) A. So: \[ R = \frac{50}{5} = 10 \, \Omega \] Step 2: Calculate the relative errors in \( V \) and \( I \).
Relative error in \( V \): \[ \frac{\Delta V}{V} = \frac{3}{50} = 0.06 \] Relative error in \( I \): \[ \frac{\Delta I}{I} = \frac{0.1}{5} = 0.02 \] Step 3: Determine the relative error in resistance \( R \).
Since \( R = \frac{V}{I} \), the relative error in \( R \) is: \[ \frac{\Delta R}{R} = \frac{\Delta V}{V} + \frac{\Delta I}{I} = 0.06 + 0.02 = 0.08 \] Step 4: Calculate the percentage error in \( R \).
The percentage error is: \[ \text{Percentage error} = \frac{\Delta R}{R} \times 100 = 0.08 \times 100 = 8% \] Final Answer: \[ \boxed{8} \]