Which one of the following measuring instruments consumes the least power?

Advantages of PMMC Instruments :

• It has a uniformly divided scale because the response of the instrument is directly proportional to the deflection of the pointer.
• Very easy to measure the quantity from that instrument.
• It has the least power consumption (25 μW to 200 μW)  among all kinds of analog instruments.
• Its torque to weight ratio is high.
• A single instrument can be used for measuring various quantities by using different values of shunts and series multipliers.

Additional Information

Permanent-Magnet Moving Coil (PMMC) Instruments:

• This instrument work on the principle that, when the current-carrying conductor placed in a magnetic field, a mechanical force acted.
• The movement of the moving coil pointer on the based of D’Arsonval movement.

Working:

• When the instrument is connected to the circuit to measure current or voltage, the measuring current flows through the coil.
• The current through the coil is placed in the magnetic field which produced a mechanical torque.
• This electrodynamic effect of mechanical torque is known as Deflecting torque.
• To control the position of the Pointer by means of Deflecting torque a hairspring is used.
• The main purpose of the hairspring is to control the deflecting torque and torque produced by it is known as Controlling torque.

Under the steady-state condition,

Controlling torque (T_c) = Deflecting torque (T_d)
Tc ∝ θ 
T_c = kθ …. (1)

Where θ is the angle of deflection made by the pointer
And, k is constant

T_d = BINA

Where, 
B is magnetic flux density in Wb / m²
I is current flow through the conductor coil in ampere
N is the number of turns of the coil
A is the area of the coil in m²

From equation (1),

kθ = BINA

\(\theta = \frac{{BINA}}{k}\)