# The derivation of the formulae for shunt and multiplier

All QuestionsThe derivation of the formulae for shunt and multiplier

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Any voltmeter will be designed so that when a known magnitude of voltage appears across it, this voltage produces a full-scale deflection (FSD) of the pointer. Any ammeter will be designed so that when a known magnitude of current passes through it, this current produces a full-scale deflection (FSD) of the pointer. In order to extend the upper limit of either of these instruments, a resistor is connected in series with the voltmeter or a resistor in parallel the ammeter. In the case of a voltmeter, the resistor is known as a multiplier; in the case of an ammeter, it is known as a shunt.
For Shunt:
I Rshunt=Rm FSD
whence:
Rshunt= IRm FSD

For Mutiplier:
FSD (Rmult+Rm)=V
and so:
Rmult=(VFSD)−Rm
Where:
FSD = Meter Full Scale Deflection
I = Current Range
V = Voltage Range
Rshunt = Shunt Resistance
Rmult = Multiplier Resistance
Rm = Meter Resistance