The formula
Shunt: R_sh = (I_g × R_g) / (I − I_g) ; Multiplier: R_s = (V / I_g) − R_g
- I_g
- full-scale deflection current of the movement (amperes)
- R_g
- resistance of the movement coil (ohms)
- I
- the new full-scale current to read (amperes)
- V
- the new full-scale voltage to read (volts)
Worked example
A movement with I_g = 1 mA and R_g = 100 Ω, extended to read 1 A and 10 V.
- Shunt: R_sh = (0.001 × 100) / (1 − 0.001) = 0.1 / 0.999
- Multiplier: R_s = (10 / 0.001) − 100 = 10000 − 100
A 0.1001 Ω shunt for the 1 A range; a 9900 Ω multiplier for the 10 V range.
Where you'll use it
Measurements papers and the practical reason a multimeter's ammeter ranges have such low resistance. It also explains loading error: a voltmeter with a low multiplier draws current and pulls down the very node it is measuring.