A voltmeter with a resistance of 1800 Ω can be used to measure the potential difference across a 200 Ω resistor. Equivalent resistance of circuit will be :

Question

Accepted Answer

To determine the equivalent resistance of the circuit when a voltmeter with a resistance of 1800 Ω is used to measure the potential difference across a 200 Ω resistor, we need to consider how these resistances are combined in the circuit.

### Explanation:

1. **Understanding the Circuit Configuration:**
   - The voltmeter is connected in parallel with the 200 Ω resistor because it is used to measure the potential difference across this resistor.
   - When resistors are in parallel, the equivalent resistance $ R_{\text{eq}} $ can be calculated using the formula:
     $$
     \frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2}
     $$
     where $ R_1 $ is the resistance of the voltmeter (1800 Ω) and $ R_2 $ is the resistance of the resistor (200 Ω).

2. **Calculating the Equivalent Resistance:**
   - Substitute the given values into the formula:
     $$
     \frac{1}{R_{\text{eq}}} = \frac{1}{1800} + \frac{1}{200}
     $$
   - Calculate each term:
     $$
     \frac{1}{1800} \approx 0.000556 \quad \text{and} \quad \frac{1}{200} = 0.005
     $$
   - Add these values:
     $$
     \frac{1}{R_{\text{eq}}} = 0.000556 + 0.005 = 0.005556
     $$
   - Find the reciprocal to get $ R_{\text{eq}} $:
     $$
     R_{\text{eq}} = \frac{1}{0.005556} \approx 180 \, \Omega
     $$

3. **Conclusion:**
   - The equivalent resistance of the circuit is approximately 180 Ω, which matches Option 1.

### Why Other Options are Incorrect:

- **Option 2 (140 Ω):** This value is incorrect because the calculation of the equivalent resistance using the parallel formula does not yield 140 Ω. The mathematical process clearly shows that the equivalent resistance is 180 Ω.

- **Option 3 (160 Ω):** Similarly, 160 Ω is not the result of the correct calculation for the parallel combination of 1800 Ω and 200 Ω. The correct calculation results in 180 Ω.

- **Option 4 (100 Ω):** This value is significantly lower than the calculated equivalent resistance. The formula and calculation steps clearly demonstrate that the equivalent resistance is 180 Ω, not 100 Ω.

In summary, the correct equivalent resistance of the circuit, when the voltmeter is connected in parallel with the 200 Ω resistor, is indeed 180 Ω, which supports Option 1 as the correct answer.