Question

The potential difference across the ends of a conductor is \( (30 \pm 0.3) V \) and the current through the conductor is \( (5 \pm 0.1) A \). The error in the determination of the resistance of the conductor is:

• A. \( 1% \)
• B. \( 2% \)
• C. \( 3% \)
• D. \( 4% \)

Hint:

When dividing two measured quantities, the percentage errors are added to obtain the overall percentage error.

Answer 1

The Correct Option is C

Step 1: Use the Formula for Resistance and Relative Error According to Ohm’s Law, resistance is given by: \[ R = \frac{V}{I}. \] The formula for the relative error in resistance is: \[ \frac{\Delta R}{R} = \frac{\Delta V}{V} + \frac{\Delta I}{I}. \]
Step 2: Substituting Given Values Given values: \[ V = 30V, \quad \Delta V = 0.3V, \quad I = 5A, \quad \Delta I = 0.1A. \] Calculating percentage errors: \[ \frac{\Delta V}{V} = \frac{0.3}{30} \times 100 = 1%. \] \[ \frac{\Delta I}{I} = \frac{0.1}{5} \times 100 = 2%. \] \[ \frac{\Delta R}{R} = 1% + 2% = 3%. \] % Final Answer Thus, the correct answer is option (3): \( 3% \).