In a permanent magnet moving coil instrument, the deflecting torque is directly proportional to-
All of the options
Understanding Deflecting Torque in PMMC Instruments
A Permanent Magnet Moving Coil (PMMC) instrument is a type of measuring instrument used to measure DC current or voltage. It works on the principle that when a current-carrying conductor is placed in a magnetic field, it experiences a force. In a PMMC instrument, a coil is placed in the magnetic field created by a permanent magnet. When current flows through the coil, it experiences a torque, known as the deflecting torque, which causes it to rotate.
Formula for Deflecting Torque
The deflecting torque ($T_d$) in a PMMC instrument is directly proportional to the magnetic field strength, the number of turns in the coil, the area of the coil, and the current flowing through the coil. The formula for the deflecting torque is given by:
$$T_d = NBIA$$
Where:
- \(N\) = Number of turns in the coil
- \(B\) = Flux density in the air gap (strength of the magnetic field)
- \(I\) = Current flowing through the coil
- \(A\) = Effective area of the coil
For a given PMMC instrument, the number of turns \(N\) and the area of the coil \(A\) are constant. The flux density \(B\) in the air gap is also ideally constant due to the permanent magnet and the core design.
Analyzing the Proportionality of Deflecting Torque
From the formula \(T_d = NBIA\), we can see how the deflecting torque is related to the given options:
- Current passing through coil (\(I\)): The formula shows a direct multiplication of \(I\). Therefore, the deflecting torque \(T_d\) is directly proportional to the current \(I\) passing through the coil, assuming N, B, and A are constant. \(T_d \propto I\).
- Flux density in air gap (\(B\)): The formula shows a direct multiplication of \(B\). Therefore, the deflecting torque \(T_d\) is directly proportional to the flux density \(B\) in the air gap, assuming N, I, and A are constant. \(T_d \propto B\).
- Number of turns of coil (\(N\)): The formula shows a direct multiplication of \(N\). Therefore, the deflecting torque \(T_d\) is directly proportional to the number of turns \(N\) of the coil, assuming B, I, and A are constant. \(T_d \propto N\).
The deflecting torque depends on all these factors directly. If any of these factors (N, B, or I) increases, the deflecting torque increases proportionally, assuming the other factors remain constant.
Evaluation of Options
Let's look at the given options in light of our analysis:
- Option 1: Current passing through coil. This is correct, as \(T_d \propto I\).
- Option 3: Flux density in air gap. This is correct, as \(T_d \propto B\).
- Option 4: Number of turns of coil. This is correct, as \(T_d \propto N\).
- Option 2: All of the options. Since options 1, 3, and 4 are all correct, this option encompasses all the factors that the deflecting torque is directly proportional to.
Therefore, the deflecting torque in a permanent magnet moving coil instrument is directly proportional to the current passing through the coil, the flux density in the air gap, and the number of turns of the coil.
Revision Table: PMMC Torque Factors
| Factor | Symbol | Relationship with \(T_d\) |
|---|---|---|
| Number of turns | \(N\) | Directly Proportional (\(T_d \propto N\)) |
| Flux density | \(B\) | Directly Proportional (\(T_d \propto B\)) |
| Current | \(I\) | Directly Proportional (\(T_d \propto I\)) |
| Area of coil | \(A\) | Directly Proportional (\(T_d \propto A\)) |
Additional Information: PMMC Instrument Components and Torque
A typical PMMC instrument consists of several key components:
- Permanent Magnet: Creates a strong, uniform magnetic field in the air gap.
- Moving Coil: A rectangular coil wound on a light aluminum former. It is pivoted so it can rotate freely.
- Control Springs: Provide a restoring or control torque (\(T_c\)) that opposes the deflecting torque. They also serve as the path for the current to the coil. The control torque is proportional to the angle of deflection (\(\theta\)), i.e., \(T_c = k\theta\), where \(k\) is the spring constant.
- Damping System: Usually eddy current damping, provided by the movement of the aluminum former in the magnetic field. This prevents oscillations and ensures the pointer settles quickly.
- Pointer and Scale: The pointer is attached to the coil and moves over a calibrated scale to indicate the measured value.
In the steady state, the deflecting torque is balanced by the control torque (\(T_d = T_c\)). Thus, \(NBIA = k\theta\). Since N, B, A, and k are constant for a given instrument, the deflection angle \(\theta\) is directly proportional to the current \(I\): \(\theta \propto I\). This linear relationship is why PMMC instruments have a uniform scale.
Understanding the factors affecting the deflecting torque is fundamental to understanding how PMMC instruments measure electrical quantities.
Important Questions from PMMC Instrument
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?
A direct voltage is applied to a peak diode voltmeter whose scale is calibrated to read rms voltage of a sine wave. If the meter reading is 36 Vrms, the value of the applied direct voltage is:
