# Torque Equation for PMMC

This post is a continuation of my previous post on Permanent magnet moving coil instruments . This post is written since a is request made by the face book user Shivany Sweet

The equation for the delevoped torque of the PMMC can be obtained from the basic law of electromagnetic torque. The deflecting torque is given by,

Where,

Therefore,

Where, G = NBA = constant

The controlling torque is provided by the springs and is proportional to the angular deflection of the pointer.

Where,

For the final steady state position,

Therefore

So, Ø = (G/K)I or I = (K/G) Ø

Thus the deflection is directly proportional to the current passing through the coil. The pointer deflection can therefore be used to measure current.

**Torque Equation for PMMC**The equation for the delevoped torque of the PMMC can be obtained from the basic law of electromagnetic torque. The deflecting torque is given by,

**Td = NBAI**Where,

**Td**= deflecting torque in N-m**B**= flux density in air gap, Wb/m2**N**= Number of turns of the coils**A**= effective area of coil m2**I**= current in the moving coil, amperesTherefore,

**Td = GI**Where, G = NBA = constant

The controlling torque is provided by the springs and is proportional to the angular deflection of the pointer.

**Tc = KØ**Where,

**Tc**= Controlling Torque**K**= Spring Constant Nm/rad or Nm/deg**Ø**= angular deflectionFor the final steady state position,

**Td = Tc**Therefore

**GI = KØ**So, Ø = (G/K)I or I = (K/G) Ø

Thus the deflection is directly proportional to the current passing through the coil. The pointer deflection can therefore be used to measure current.

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