The DC current flowing in a circuit is measured by two ammeters, one PMMC and another electrodynamometer type, connected in series. The PMMC meter contains 100 turns in the coil, the flux density in the air gap is 0.2 ωb/m2 and the area of the coil is 80 mm2. The electrodynamometer ammeter has a change in mutual inductance with respect to deflection of 0.5mH/deg the spring constants of both the meters are equal. The value of current, at which the deflection of the two meters are same, is – (in A)
Concept:
PMMC Instrument:
In PMMC instruments, the deflecting torque is given by
Td = BINA
Where Td = Deflecting torque in N-m
B = Flux density, wb/m2
I = Current in the Coil, amperes
N = number of turns of the coil
A = Effective coil area m2
Dynamometer Ammeter:
The deflection torque of the dynamometer ammeter is given by
\({T_d} = {I^2}\frac{{dM}}{{dθ }}\)
Where,
I = fixed or current coil current
dM = change in mutual inductance
dθ = change in deflection
Calculation:
Both the PMMC and Electrodynammter type ammeters are in series therefore they measure the same amount of current and have the same deflecting torques (same spring constants and deflection in both the instruments)
Deflecting torque in PMMC = Deflecting torque in Electrodynamomter type instrument
\(BINA = I^2 \frac{dm}{dθ}\)
0.2 I (80 x 10-6) x 100 = I2 x 0.5 x 10-3
I = 3.2 A
Important Questions from PMMC Instrument
In a permanent magnet moving coil instrument, the deflecting torque is directly proportional to-
Which of the following types of damping is used in a permanent magnet moving coil instrument?
Which of the following measurement instruments consumes the least amount of energy?
In the below given deflecting torque equation “B” indicates:
Equation: Deflecting torque = N.B.A.I
Which of the following is the disadvantage of PMMC instruments?
