The Moving Coil Galvanometer

To solve this problem, we need to understand the working principle of a moving coil galvanometer. The deflection in a moving coil galvanometer is directly proportional to the current flowing through it. This is based on the principle that the torque on a coil in a magnetic field is proportional to the current and the number of turns in the coil.

The deflection can be represented as:

Given:

• A current of 200 produces a deflection of .
• We need to find the current that causes a deflection through radians.

First, convert to radians:

Using the proportionality, write the equation for both scenarios:

Equating the ratios as the proportionality constant is the same:

Simplify the right-hand side:

Thus, the equation becomes:

Cross-multiply to solve for :

Therefore, the current required to cause a deflection of radians is 60 .

Hence, the correct option is 60 .

To convert a galvanometer into an ammeter, a low resistance called a "shunt" is connected in parallel with the galvanometer. The shunt resistance allows the ammeter to measure larger currents by diverting most of the current around the galvanometer.

Given:

• Resistance of the galvanometer coil,
• Full scale deflection current of the galvanometer,
• Desired range of the ammeter,

The current flowing through the shunt resistor, , is given by:

Substitute the values:

The voltage across the galvanometer and the shunt is the same. Therefore, we have:

We can rearrange to find the shunt resistance, :

Substitute the values:

Calculate the value:

Therefore, the value of the resistance to be added so the galvanometer can be used as an ammeter with a range of 0-20 mA is .

The correct answer is: .

To solve this problem, we need to find the resistance of a moving coil galvanometer using the concept of shunt resistance. A shunt is applied to decrease the deflection, and we can use the following formula:

The deflection of a galvanometer is proportional to the current passing through it. Therefore, the deflection is inversely proportional to the shunt resistance applied.

Given:

• Initial deflection, divisions
• Final deflection, divisions
• Shunt resistance,

Using the formula based on proportionality of deflections:

Where is the resistance of the galvanometer coil.

Substituting the given values into the formula, we have:

Simplifying the equation:

Thus,

Rearranging the terms gives:

Finally, solving for (the resistance of the galvanometer):

Thus, the resistance of the galvanometer coil, , is .

The correct answer is, therefore, .

Let's analyze each statement to determine which ones are correct:

Statement Analysis:

A: The torsional constant in moving coil galvanometer has dimensions

• The torsional constant ( ) is the restoring force per unit angular displacement and is expressed in terms of torque per radian. Torque has dimensions , which confirms this statement is correct.

B: Increasing the current sensitivity may not necessarily increase the voltage sensitivity.

• Current sensitivity of a galvanometer is defined as the deflection per unit current ( ). Voltage sensitivity is defined as the deflection per unit voltage ( ). By Ohm's law, , we get that voltage sensitivity depends on both current sensitivity and resistance of the galvanometer. Hence, increasing current sensitivity doesn't necessarily increase voltage sensitivity as resistance can vary, making this statement correct.

C: If we increase the number of turns to its double , then the voltage sensitivity doubles.

• Voltage sensitivity depends linearly on the number of turns through but inversely with the resistance . If is doubled, while current sensitivity doubles, resistance also doubles, keeping voltage sensitivity constant. Thus, this statement is incorrect.

D: MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with the galvanometer.

• To convert a galvanometer into an ammeter, a low-value shunt resistance is added in parallel. This allows most of the current to bypass the galvanometer since ammeters measure large currents. Thus, this statement is incorrect.

E: Current sensitivity of MCG depends inversely on the number of turns of the coil.

• Current sensitivity is , where is the number of turns, is magnetic field strength, is the area of the coil, and is torsional constant. Clearly, current sensitivity is directly proportional to , not inversely. Thus, this statement is incorrect.

Conclusion:

• Only statements A and B are correct, which matches the given correct answer: A, B only.