Question 137: Current Electricity

Question

Consider a moving coil galvanomenter (MCG):
A. The torsional constant in moving coil galvanometer has dimensions $\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$
B. Increasing the current sensitivity may not necessarily increase the voltage sensitivity.
C. If we increase number of turns $(\mathrm{N})$ to its double $(2 \mathrm{~N})$, then the voltage sensitivity doubles.
D. MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer.
E. Current sensitivity of MCG depends inversely on number of turns of coil.
Choose the correct answer from the options given below:

Accepted Answer

Let's analyze each statement step by step.
Statement A: Ã¢ÂÂThe torsional constant in moving coil galvanometer has dimensions $$[ML^2T^{-2}]$$.Ã¢ÂÂ
The torsional constant (often denoted by $$k$$) relates the restoring torque to the angular displacement via $$	au = k 	heta$$. Since torque has dimensions of force ÃÂ distance with dimensions $$[MLT^{-2} 	imes L = ML^2T^{-2}]$$ and the angular displacement (in radians) is dimensionless, the torsional constant indeed has the dimensions $$[ML^2T^{-2}]$$.
Thus, Statement A is correct.
Statement B: Ã¢ÂÂIncreasing the current sensitivity may not necessarily increase the voltage sensitivity.Ã¢ÂÂ
The current sensitivity of a galvanometer is defined as its deflection per unit current (i.e. $$	heta/I$$).
The voltage sensitivity, on the other hand, is the deflection per unit applied voltage when the galvanometer is used as a voltmeter. This sensitivity is proportional to the current sensitivity divided by the galvanometerÃ¢ÂÂs internal resistance.
Often, if you try to increase current sensitivity (for instance, by increasing the number of turns or enhancing the magnetic field), the internal resistance may also change (typically increase when number of turns is increased). Therefore, the improvement in current sensitivity does not automatically translate to a proportional increase in voltage sensitivity.
Hence, Statement B is true.
Statement C: Ã¢ÂÂIf we increase number of turns ($$N$$) to its double ($$2N$$), then the voltage sensitivity doubles.Ã¢ÂÂ
The deflection (current sensitivity) is proportional to $$N$$ since $$	heta \propto N I$$.
However, when you double $$N$$, the length of the wire increases, and so does the internal resistance (approximately doubling it, assuming the wire diameter and material remain the same).
Since voltage sensitivity is roughly given by $$\frac{	ext{current sensitivity}}{	ext{internal resistance}} \propto \frac{N}{R_g}$$, if both $$N$$ and $$R_g$$ double, the ratio remains essentially unchanged.
Therefore, doubling $$N$$ does not double the voltage sensitivity, so Statement C is incorrect.
Statement D: Ã¢ÂÂMCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer.Ã¢ÂÂ
To convert a galvanometer into an ammeter, a shunt resistor is used to bypass most of the current so that only a small fraction (the fullÃ¢ÂÂscale deflection current) passes through the galvanometer.
For this to work, the shunt resistance should be very low compared to the galvanometerÃ¢ÂÂs resistance, not of Ã¢ÂÂlarge value.Ã¢ÂÂ
Therefore, Statement D is false.
Statement E: Ã¢ÂÂCurrent sensitivity of MCG depends inversely on number of turns of coil.Ã¢ÂÂ
As mentioned before, the electromagnetic torque in the coil is given by $$	au_e \propto N I$$, so the deflection per unit current is $$	heta/I \propto N$$.
This shows that the current sensitivity increases with $$N$$ (i.e. it is directly proportional to $$N$$), not inversely.
Hence, Statement E is false.
Only Statements A and B are correct.
Looking at the given options, the correct choice is:
Option B: A, B Only.

Answer

A, D Only

Answer

A, B Only

Answer

A, B, E Only

Answer

B, D, E Only

Current Electricity

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