The resistance R of a metallic conductor is equal to the ratio of potential difference V across the resistor to the current I through the conductor. Calculate R given tat `V=(11.1+-0.1)` volt and `I=(5.5+-0.5)A`

Explanation

To solve the problem, we need to calculate the resistance \( R \) using the formula \( R = \frac{V}{I} \), where \( V \) is the potential difference and \( I \) is the current. We are also required to calculate the uncertainty in the resistance \( \Delta R \).

### Step 1: Calculate the Resistance \( R \)

1. **Given Values**:
- \( V = 11.1 \pm 0.1 \) volts
- \( I = 5.5 \pm 0.5 \) A

2. **Using the formula for resistance**:
\[ R = \frac{V}{I} \]

3. **Substituting the values**:
\[ R = \frac{11.1}{5.5} \]

4. **Calculating \( R \)**:
\[ R = 2.01818 \approx 2.0 \quad \text{(keeping 2 significant figures)} \]

### Step 2: Calculate the Uncertainty in Resistance \( \Delta R \)

1. **Using the formula for uncertainty**:
\[ \frac{\Delta R}{R} = \frac{\Delta V}{V} + \frac{\Delta I}{I} \]

2. **Substituting the uncertainties**:
- \( \Delta V = 0.1 \)
- \( \Delta I = 0.5 \)

3. **Calculating \( \Delta V/V \)**:
\[ \frac{\Delta V}{V} = \frac{0.1}{11.1} \approx 0.00901 \]

4. **Calculating \( \Delta I/I \)**:
\[ \frac{\Delta I}{I} = \frac{0.5}{5.5} \approx 0.09091 \]

5. **Adding the uncertainties**:
\[ \frac{\Delta R}{R} = 0.00901 + 0.09091 \approx 0.09992 \]

6. **Calculating \( \Delta R \)**:
\[ \Delta R = R \times 0.09992 \approx 2.0 \times 0.09992 \approx 0.19984 \approx 0.2 \quad \text{(keeping 1 significant figure)} \]

### Final Result

Thus, the resistance \( R \) with its uncertainty is:
\[ R = 2.0 \pm 0.2 \, \Omega \]