Chapter 2, Problem 2.98IP

Analog Voltmeter Design
Figure P2-98(a) shows a voltmeter circuit consisting of a D'Arsonval meter, two series resistors, and a two-position selector switch. A current of $I_{\text{FS}}=400\text{μΑ}$ produces full-scale deflection of the D'Arsonval meter, whose internal resistance is $R_M=25\Omega .$

1. Select the series resistance $R_1$ and $R_2$ so that a voltage $v_x=100\text{V}$ produces full-scale deflection when the switch is in position As and voltage $v_x=10\text{V}$ produces full-scale deflection when the switch is in position B.
2. What is the voltage across the $20\text{-kΩ}$ resistor in Figure P2-98(b)? What is the voltage when the voltmeter in part (a) is set to position A and connected across the $20\text{-kΩ}$ resistor? What is the percentage error introduced connecting the voltmeter?
3. A different D'Arsonval meter is available with an internal resistance of $100\Omega$ and a full-scale deflection current of $100\text{μΑ}\text{.}$ If the voltmeter in part (a) is redesigned using this D' Arsonval meter, would the error found in part (b) be smaller or larger? Explain.