To extend the useful range of a voltmeter an additional resi

To extend the useful range of a voltmeter, an additional resistor, R_series. is placed in series with the voltmeter as shown in the figure. If the internal resistance of the voltmeter is Ri.V. determine the resistance that the added series resistor has to have to extend the useful range of the voltmeter. Then, calculate the resistance the series resistor has to have to allow a voltmeter with an internal resistance of 2.00 M Ohm (10_6 Ohm) and a maximum range of 2.00 V to measure potential differences up to 200. V

Solution

Maximum range of Voltmeter = 2V

I_max = V_max / R_iV = 2 / 2x10⁶ A = 10^-6 A

New range of Voltemeter after adding series resistance R_series,

V_max,new = I_max (R_iV + R_series)

Hence, R_series = (V_max,new / I_max) - R_iV = (200/10^-6) - 2x10⁶ = 198 M-ohm