### 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

**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, amperes

Therefore, **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 deflection

For 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.