A moving-coil galvanometer is converted into a voltmeter by increasing its effective resistance by connecting a high resistance Rs in series with the galvanometer, shown in figure. The series resistance is also useful for changing the range of any given voltmeter.
A voltmeter is a modified galvanometer
Let G be the resistance of the galvanometer coil and Ig the current required for a full-scale deflection.
Let V be the maximum potential difference to be measured. The value of the series resistance Rs should be such that when the potential difference applied across the instrument is V, the current through the galvanometer is Ig .
In the series combination, the potential difference V gets divided across the galvanometer (resistance, G) and the resistance Rs :
V = IgG + IgRs = Ig (G + Rs)
∴ Rs = \(\cfrac{V}{I_g}\) – G
This is the required value of the series resistance. The scale of the galvanometer is then calibrated so as to read the potential difference in volt or its submultiples, e.g., mV, directly.
[Notes : (1) A series multiplier is made of manganin wire because manganin has a very small temperature coefficient of resistivity. (2) The maximum potential difference Vg that can be dropped across the galvanometer is Vg = Ig G. Therefore, the above expression for the series resistance may be rewritten as
RS = \(\cfrac{VG}{I_gG}\) - G
= \(\cfrac{VG}{V_g}\) - G = G(P-1)
where p = V/Vg is the range-multiplying factor, i.e., the voltage range of the galvanometer can be increased by a factor of p by connecting a series resistance which is (p – 1) times the galvanometer resistance.
∴ p = \(\cfrac{V}{V_g}\) = \(\cfrac{(R_S+G)I_g}{GI_g}\) = \(\cfrac{R_S+G}G\)
Since the resistance of the voltmeter is RV = RS + G,
P = \(\cfrac{R_V}G\)
∴ RV = GP]
