Question

In an electrical circuit, the voltage is measured as V = (200 ± 4) volt and the current is measured as I = (20 ± 0.2) A. The value of the resistance is:

• A. (10 ± 4.2) Ω
• B. (10 ± 0.3) Ω
• C. (10 ± 0.1) Ω
• D. (10 ± 0.8) Ω

Answer 1

The Correct Option is B

1. Calculate Resistance $R$

Using Ohm's Law: 

$$ R = \frac{V}{I} = \frac{200 \, \text{V}}{20 \, \text{A}} = 10 \, \Omega $$

2. Error propagation formula

For $R = V/I$, fractional errors add:

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

Given: $\Delta V = 4 \, \text{V}$, $\Delta I = 0.2 \, \text{A}$

3. Calculate fractional error

$$ \frac{\Delta R}{10} = \frac{4}{200} + \frac{0.2}{20} $$

$$ \frac{\Delta R}{10} = 0.02 + 0.01 = 0.03 $$

4. Find absolute error $\Delta R$

$$ \Delta R = 0.03 \times 10 = 0.3 \, \Omega $$

Thus, $R = (10 \pm 0.3) \, \Omega$