Voltmeter Resistance Calculation Explained

This question asks us to find the total resistance of a voltmeter given its voltage range and sensitivity. Understanding voltmeter characteristics is crucial for accurate electrical measurements.

Understanding Voltmeter Sensitivity

Voltmeter sensitivity is a measure of how much resistance is present for each volt of the voltmeter's measuring range. It's typically expressed in units of kilo-ohms per volt (kΩ/V). A higher sensitivity means the voltmeter draws less current from the circuit being measured, leading to more accurate readings, especially in high-impedance circuits.

Calculating Total Voltmeter Resistance

The total internal resistance of a voltmeter ($R_{total}$) can be calculated using its sensitivity ($S$) and its full-scale voltage range ($V_{range}$). The formula is:

$R_{total} = S \times V_{range}$

Step-by-Step Calculation

We are given the following values:

• Voltmeter Range ($V_{range}$): 50 V
• Voltmeter Sensitivity ($S$): 20 kΩ/V

Now, let's plug these values into the formula:

$R_{total} = (20 \text{ kΩ/V}) \times (50 \text{ V})$

Multiplying the sensitivity by the voltage range:

$R_{total} = 1000 \text{ kΩ}$

Converting Units

To express the total resistance in mega-ohms (MΩ), we know that 1 MΩ = 1000 kΩ.

$R_{total} = \frac{1000 \text{ kΩ}}{1000 \text{ kΩ/MΩ}} = 1 \text{ MΩ}$

Conclusion

Therefore, the total resistance of the voltmeter is 1 MΩ. This value corresponds to option 2.