(II) A particular digital meter is based on an electronic...

(II) A particular digital meter is based on an electronic module that has an internal resistance of 100 $\mathrm{MS}$ and a full-scale sensitivity of 400 $\mathrm{mV}$ . Two resistors connected as shown in Fig. 63 can be used to change the voltage range. Assume $R_{1}=10 \mathrm{M} \Omega$ . Find the value of $R_{2}$ that will result in a voltmeter with a full-scale range of 40 $\mathrm{V} .$

Key Concepts

Voltage Divider Principle

The voltage divider principle is a fundamental concept where two or more resistors are used in series to scale down a higher voltage to a desired lower voltage. This principle is crucial in designing measurement circuits where the full-scale input of a device must be matched or adjusted to accommodate a different range of input voltages.

Resistor Network Design for Range Extension

This involves using additional resistors in series or parallel with an instrument to expand its measurement range. By carefully selecting resistor values in conjunction with the device’s inherent characteristics like internal resistance and sensitivity, the effective range of the instrument can be increased, making it suitable for measuring larger voltages without compromising accuracy.

Full-Scale Sensitivity

This is the voltage or current level required at the meter’s input to produce a maximum (or full-scale) reading. It is a key specification of measurement devices as it defines the limit of the instrument’s response and helps determine how external components, like resistors, are needed to adapt the instrument to measure signals beyond its inherent sensitivity.

Internal Resistance

The internal resistance of a meter is the resistance that is inherently present within an instrument. It plays an important role in determining how the instrument interacts with the rest of the circuit, affecting the voltage drop and overall accuracy of the measurements when additional circuit elements are attached.

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