Question

If across a resistance, voltage applied is \((20 \pm 0.2)\,\text{V}\) and the current passing through it is \((10 \pm 0.1)\,\text{A}\). Find the maximum error in resistance.

• A. \(0.04\)
• B. \(0.05\)
• C. \(0.06\)
• D. \(0.07\)

Hint:

For multiplication or division of quantities: \[ \frac{\Delta Z}{Z} = \frac{\Delta A}{A} + \frac{\Delta B}{B} \] Always add fractional errors.

Answer 1

The Correct Option is A

Concept: From Ohm's law \[ V = IR \] \[ R = \frac{V}{I} \] Maximum fractional error rule: \[ \frac{\Delta R}{R} = \frac{\Delta V}{V} + \frac{\Delta I}{I} \]
Step 1: Calculate resistance. \[ R = \frac{V}{I} \] \[ R = \frac{20}{10} \] \[ R = 2\,\Omega \]
Step 2: Calculate fractional error. \[ \frac{\Delta R}{R} = \frac{0.2}{20} + \frac{0.1}{10} \] \[ \frac{\Delta R}{R} = 0.01 + 0.01 \] \[ \frac{\Delta R}{R} = 0.02 \]
Step 3: Find maximum error in resistance. \[ \Delta R = R \times 0.02 \] \[ \Delta R = 2 \times 0.02 \] \[ \Delta R = 0.04 \] \[ \boxed{\Delta R = 0.04} \]