Instrument Sensitivity and Internal Resistance Explained

This question asks us to find the internal resistance of an electrical instrument given its sensitivity and the voltage scale it's operating on. Understanding the relationship between these parameters is key to solving this problem.

Understanding Instrument Sensitivity

Instrument sensitivity is a crucial specification that tells us how much the instrument's reading changes for a given change in the measured quantity. For voltmeters and ohmmeters, sensitivity is often expressed in units of ohms per volt (Ω/V). A higher sensitivity value generally indicates a more accurate instrument, especially for older analog types, as it implies a higher internal resistance, which draws less current from the circuit being measured.

The sensitivity in ohms per volt is essentially the total resistance of the instrument (often referred to as its internal resistance when used as a voltmeter) divided by the full-scale voltage reading of the selected range.

Calculating Internal Resistance

We can express the relationship using the following formula:

$$ \text{Sensitivity} (\Omega/\text{V}) = \frac{\text{Internal Resistance} (\Omega)}{\text{Full-Scale Voltage} (\text{V})} $$

To find the internal resistance, we can rearrange this formula:

$$ \text{Internal Resistance} (\Omega) = \text{Sensitivity} (\Omega/\text{V}) \times \text{Full-Scale Voltage} (\text{V}) $$

Applying the Formula

Let's plug in the values given in the question:

• Sensitivity = 1000 Ω/V
• Full-Scale Voltage = 100 V

Now, we calculate the internal resistance:

$$ \text{Internal Resistance} = 1000 \, \Omega/\text{V} \times 100 \, \text{V} $$

$$ \text{Internal Resistance} = 100,000 \, \Omega $$

Result Analysis

The calculated internal resistance of the instrument on the 100-volt scale is 100,000 ohms. This value aligns with one of the provided options.