Consider a moving coil galvanometer (MCG): A: The torsional constant in moving coil galvanometer has dimensions [ML^2 T^

Question

Consider a moving coil galvanometer (MCG): A: The torsional constant in moving coil galvanometer has dimensions [ML^2 T^-2] B: Increasing the current sensitivity may not necessarily increase the…

Accepted Answer

Given: We must check the correctness of statements A to E for a moving coil galvanometer.

Find: Which set of statements is correct.

For a moving coil galvanometer, current sensitivity is

\frac{\theta}{I} = \frac{NBA}{k}

and voltage sensitivity is

\frac{\theta}{V} = \frac{\theta}{I} \cdot \frac{I}{V} = \frac{NBA}{kR}

where $N$ is the number of turns, $B$ is magnetic field, $A$ is coil area, $k$ is torsional constant, and $R$ is galvanometer resistance.

Statement A: The torsional constant is torque per unit angular displacement. Since angular displacement is dimensionless, its dimensions are the same as torque:

[ML^2T^{-2}]

So A is correct.

Statement B: Voltage sensitivity depends on both current sensitivity and resistance:

\frac{\theta}{V} = \frac{1}{R}\frac{\theta}{I}

Therefore, increasing current sensitivity does not always increase voltage sensitivity because $R$ can also change. So B is correct.

Statement C: If $N$ is doubled, then current sensitivity doubles because

\frac{\theta}{I} = \frac{NBA}{k}

but resistance also increases with the number of turns. Hence voltage sensitivity

\frac{\theta}{V} = \frac{NBA}{kR}

does not necessarily double; it can remain unchanged. So C is incorrect.

Statement D: To convert a galvanometer into an ammeter, a low-value shunt resistance is connected in parallel so that most of the current bypasses the galvanometer. Therefore the statement saying large value shunt is used is false. So D is incorrect.

Statement E: From

\frac{\theta}{I} = \frac{NBA}{k}

current sensitivity is directly proportional to $N$ , not inversely proportional to $N$ . So E is incorrect.

Therefore, only statements A and B are correct. The correct option is A.

Given: A set of five statements about a moving coil galvanometer.

Find: Which statements are true.

A is true because torsional constant is measured as restoring torque per unit angular twist, and torque has dimensions $[ML^2T^{-2}]$ .
B is true because voltage sensitivity depends on both current sensitivity and galvanometer resistance.
C is false because doubling $N$ also changes resistance, so voltage sensitivity does not necessarily double.
D is false because an ammeter requires a small shunt resistance in parallel, not a large one.
E is false because current sensitivity is directly proportional to the number of turns:

\frac{\theta}{I} = \frac{NBA}{k}

Hence only A and B are correct.

Answer

Step-by-step solution

Common mistakes

Practice more PN Junction & Zener Characteristics questions