A voltmeter has a least count of 0.1 V and an ammeter has a least count of 0.1 A. The potential drop V across a resistance is measured as 10.0 V and current through it is measured as 1.0 A .Select the correct alternative

Options

A. The value of R is `(1.0 pm 0.1) xx10^1 Omega`
B. The relative error in measurement of current is `1/10`
C. The accuracy in measurement of potential drop is `1/100`
D. The value of R is `(10+0.2) Omega`

Answer

To solve the problem step-by-step, we will analyze the measurements and calculate the resistance and its associated errors.

### Step 1: Identify the given values
- Least count of voltmeter (ΔV) = 0.1 V
- Least count of ammeter (ΔI) = 0.1 A
- Voltage measured (V) = 10.0 V
- Current measured (I) = 1.0 A

### Step 2: Calculate the resistance using Ohm's Law
According to Ohm's Law:
\[ R = \frac{V}{I} \]

Substituting the values:
\[ R = \frac{10.0 \, \text{V}}{1.0 \, \text{A}} = 10.0 \, \Omega \]

### Step 3: Calculate the error in the resistance measurement
To find the error in the resistance (ΔR), we use the formula for the propagation of errors:
\[ \frac{\Delta R}{R} = \frac{\Delta V}{V} + \frac{\Delta I}{I} \]

Substituting the known values:
- ΔV = 0.1 V
- V = 10.0 V
- ΔI = 0.1 A
- I = 1.0 A

Calculating the relative errors:
\[ \frac{\Delta R}{10} = \frac{0.1}{10} + \frac{0.1}{1} \]
\[ \frac{\Delta R}{10} = 0.01 + 0.1 = 0.11 \]

### Step 4: Solve for ΔR
Now, multiply both sides by 10:
\[ \Delta R = 10 \times 0.11 = 1.1 \, \Omega \]

### Step 5: Write the final result for resistance with error
Thus, the resistance can be expressed as:
\[ R = 10.0 \pm 1.1 \, \Omega \]

### Step 6: Format the answer
This can also be expressed in scientific notation:
\[ R = 1.0 \pm 0.1 \times 10^1 \, \Omega \]

### Step 7: Verify the options
1. **Option 1**: \( R = 1.0 \pm 0.1 \times 10^1 \, \Omega \) is correct.
2. **Option 2**: Relative error in current \( \frac{\Delta I}{I} = \frac{0.1}{1} = 0.1 \) or \( \frac{1}{10} \) is correct.
3. **Option 3**: Accuracy in potential drop \( \frac{\Delta V}{V} = \frac{0.1}{10} = 0.01 \) or \( \frac{1}{100} \) is correct.
4. **Option 4**: \( R = 10 \pm 0.2 \) is incorrect.

### Conclusion
The correct alternatives are options 1, 2, and 3.

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