When a current of `(2.5 +- 0.5)` ampere flows through a wire, it develops a potential difference of `(20 +- 1)` volt, the resistance of the wire is

Options

A. `(8 pm 2)Omega`
B. `(8 pm 1.6)Omega`
C. `(8 pm 1.5)Omega`
D. `(8 pm 3)Omega`

Answer

To find the resistance of the wire when a current of \( (2.5 \pm 0.5) \) amperes flows through it, and it develops a potential difference of \( (20 \pm 1) \) volts, we can follow these steps:

### Step 1: Use Ohm's Law
According to Ohm's Law, the resistance \( R \) can be calculated using the formula:
\[ R = \frac{V}{I} \]
where \( V \) is the potential difference and \( I \) is the current.

### Step 2: Substitute the Values
Substituting the values for \( V \) and \( I \):
\[ R = \frac{20 \text{ volts}}{2.5 \text{ amperes}} = 8 \text{ ohms} \]

### Step 3: Calculate the Error in Resistance
To find the error in resistance \( \Delta R \), we use the formula:
\[ \frac{\Delta R}{R} = \frac{\Delta V}{V} + \frac{\Delta I}{I} \]
where:
- \( \Delta V = 1 \) volt (error in voltage)
- \( V = 20 \) volts (measured voltage)
- \( \Delta I = 0.5 \) amperes (error in current)
- \( I = 2.5 \) amperes (measured current)

### Step 4: Substitute the Errors
Substituting the values into the error formula:
\[ \frac{\Delta R}{8} = \frac{1}{20} + \frac{0.5}{2.5} \]

### Step 5: Simplify the Right Side
Calculating each term on the right side:
\[ \frac{1}{20} = 0.05 \]
\[ \frac{0.5}{2.5} = 0.2 \]
So,
\[ \frac{\Delta R}{8} = 0.05 + 0.2 = 0.25 \]

### Step 6: Solve for \( \Delta R \)
Now, multiply both sides by 8 to find \( \Delta R \):
\[ \Delta R = 8 \times 0.25 = 2 \text{ ohms} \]

### Step 7: Final Result
Thus, the resistance of the wire is:
\[ R = 8 \pm 2 \text{ ohms} \]