Question

In a moving coil instruments, the deflecting torque is proportional to:

• A. \( I^2 \)
• B. \( I \)
• C. \( V \)
• D. Power

Hint:

PMMC \( \implies T_d \propto I \) (Linear scale).
Moving Iron/Electrodynamometer \( \implies T_d \propto I^2 \) (Non-linear scale).
This basic contrast is highly tested in electrical measurements.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks to identify the relationship between the deflecting torque (\( T_d \)) and the operating electrical current (\( I \)) in a Permanent Magnet Moving Coil (PMMC) instrument.
PMMC is a highly precise instrument used for measuring direct currents (DC).

Step 2: Key Formula or Approach:
The deflecting torque produced in a moving coil instrument placed in a uniform magnetic field is given by the electromagnetic force equation:
\[ T_d = B \cdot I \cdot A \cdot N \] Where:
\( B \) is the magnetic flux density of the permanent magnet in \( \text{Wb/m}^2 \)
\( I \) is the current flowing through the coil in Amperes
\( A \) is the active area of the coil in \( \text{m}^2 \)
\( N \) is the number of turns of wire on the moving coil

Step 3: Detailed Explanation:
Let us examine the implications of this torque equation:

• Constant Parameters: For a constructed instrument, the parameters \( B, A, \) and \( N \) are physical constants.
Therefore, the deflecting torque equation simplifies to:
\[ T_d \propto I \]
• Scale Linearization: A controlling torque (\( T_c \)) is provided by springs, which is proportional to the pointer deflection angle (\( \theta \)):
\[ T_c = k \theta \] At the steady-state balanced position:
\[ T_d = T_c \implies BIAN = k \theta \implies \theta = \left(\frac{BAN}{k}\right) I \] This directly shows that the deflection angle \( \theta \) is linearly proportional to the current \( I \).
As a consequence, moving coil instruments have a perfectly uniform and linear scale.

Step 4: Final Answer:
In moving coil instruments, the deflecting torque is directly proportional to the current \( I \).