The resistance of an ideal voltmeter is

Options

A. Zero
B. Infinity
C. `1000 Omega`
D. `10000Omega`

Answer

To determine the resistance of an ideal voltmeter, we can follow these steps:

### Step 1: Understand the Function of a Voltmeter
A voltmeter is used to measure the potential difference (voltage) across two points in a circuit. It is always connected in parallel with the component across which the voltage is to be measured.

**Hint:** Remember that voltmeters measure voltage by being connected across components in a circuit.

### Step 2: Analyze the Circuit Configuration
When a voltmeter is connected in parallel with a resistor, it creates a situation where the voltmeter should ideally not draw any current from the circuit. This means that all the current should flow through the resistor.

**Hint:** Think about what happens to the current when a voltmeter is connected in parallel.

### Step 3: Define the Ideal Condition
For an ideal voltmeter, the current flowing through it (let's call it I1) should be equal to 0. This ensures that the voltmeter does not affect the circuit operation and that the voltage measured is solely across the resistor.

**Hint:** Consider the implications of a voltmeter drawing no current on the circuit.

### Step 4: Apply Ohm’s Law
Using Ohm's Law, we can express the relationship between voltage (V), current (I), and resistance (R) as:
\[ V = I \times R \]
For the voltmeter, we can rearrange this to find the resistance of the voltmeter (Rv):
\[ R_v = \frac{V_{AB}}{I_1} \]

**Hint:** Recall that Ohm's Law relates voltage, current, and resistance.

### Step 5: Substitute the Ideal Condition
Since we established that for an ideal voltmeter, I1 = 0, substituting this into the equation gives:
\[ R_v = \frac{V_{AB}}{0} \]
This indicates that the resistance of the voltmeter approaches infinity.

**Hint:** Think about what happens mathematically when you divide by zero.

### Step 6: Conclusion
Thus, the resistance of an ideal voltmeter is considered to be infinite. This means it does not draw any current from the circuit, allowing it to measure the voltage accurately without affecting the circuit.

**Final Answer:** The resistance of an ideal voltmeter is infinity.