The Ammeter and the Voltmeter — Question 2

Question 2

A series multiplier sets a voltmeter range through the movement current

A movement has resistance Rg=1.00 kilohm and full-scale current Ig=100 microampere. A series resistor Rs makes a 20.0 V full-scale voltmeter.

1. Find Rs and the total input resistance.

2. Find the movement voltage and the power dissipated in Rs at full scale.

Question 2 - Solution

A series multiplier sets a voltmeter range through the movement current

(a) Method and calculation

$$R_V=V_{\mathrm{FS}}/I_g=20/(10^{-4})=200\,\mathrm{k\Omega}.$$$$R_s=R_V-R_g=199\,\mathrm{k\Omega}.$$

(b) Interpretation and further calculation

$$V_g=I_gR_g=.100\,\mathrm V,\quad V_s=20-.100=19.9\,\mathrm V.$$$$P_s=I_g^2R_s=1.99\times10^{-3}\,\mathrm W.$$

Physical check

A large input resistance reduces the extra current drawn by a voltmeter.