Q2Electronic Measurement & Instrumentation

A Permanent Magnet Moving Coil (PMMC) instrument is the most accurate type for DC measurement. It consists of: 1. A strong U-shaped permanent magnet with soft iron pole pieces. 2. A soft iron cylindrical core placed between the poles to make the magnetic field uniformly radial. 3. A rectangular moving coil of fine wire wound on a lightweight aluminum former, free to rotate around the core. 4. A pointer attached to the coil spindle moving over a graduated scale.

When current $I$ flows through the coil of $N$ turns and area $A$, placed in a radial magnetic field of flux density $B$, the Deflecting Torque ($T_d$) is: $T_d=BINA$

(i) With Spring Control: Two hairsprings provide a restoring torque directly proportional to the angle of deflection $\theta$. $T_c=K\theta$ (where $K$ is the spring constant). At equilibrium, $T_d=T_c$: $BINA=K\theta ⟹\theta =\left(\frac{BNA}{K}\right)I$ Since the terms in the bracket are constant, $\theta \propto I$. The scale is perfectly linear.

(ii) With Gravity Control: Small weights are attached to the pointer. As the pointer deflects by $\theta$, gravity provides a restoring torque proportional to the sine of the angle. $T_c=WL\sin \theta$ (where $W$ is weight and $L$ is distance from pivot). At equilibrium, $T_d=T_c$: $BINA=WL\sin \theta ⟹\sin \theta =\left(\frac{BNA}{WL}\right)I$ Here, $\sin \theta \propto I$. Because of the sine relationship, the scale is non-linear, being compressed (crowded) at the upper end.