Explain: "Increasing the current sensitivity may not necessarily increase the voltage sensitivity".

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) Current sensitivity of a galvanometer is defined as the deflection per unit current, given by:
$\frac{\phi}{I} = \frac{NAB}{k} \quad \dots (1)$
where $N$ is the number of turns, $A$ is the area, $B$ is the magnetic field, and $k$ is the torsional constant.
If we double the number of turns $(N \rightarrow 2N)$, the current sensitivity becomes:
$\left(\frac{\phi}{I}\right)' = \frac{(2N)AB}{k} = 2 \left(\frac{\phi}{I}\right)$
Thus, the current sensitivity doubles.
However, the resistance $R$ of the galvanometer coil is proportional to the length of the wire. Since the length of the wire is proportional to the number of turns, doubling the turns also doubles the resistance $(R \rightarrow 2R)$.
Voltage sensitivity is defined as the deflection per unit voltage, given by:
$\frac{\phi}{V} = \frac{\phi}{IR} = \left(\frac{NAB}{k}\right) \frac{1}{R}$
If $N$ is doubled, $R$ also doubles. Substituting these into the voltage sensitivity formula:
$\left(\frac{\phi}{V}\right)' = \frac{(2N)AB}{k(2R)} = \frac{NAB}{kR} = \frac{\phi}{V}$
Therefore, the voltage sensitivity remains unchanged. This proves that increasing current sensitivity does not necessarily increase voltage sensitivity.

Explore More

Similar Questions

An ammeter reads up to $1\, A$. Its internal resistance is $0.81\, \Omega$. To increase the range to $10\, A$,the value of the required shunt is ............ $\Omega$.

The resistance of a $1\, A$ ammeter is $0.018\,\Omega$. To convert it into a $10\, A$ ammeter,the shunt resistance required will be:

In the given figure,an ammeter $A$ consists of a $240 \Omega$ coil connected in parallel to a $10 \Omega$ shunt. The reading of the ammeter is . . . . . . $mA$.

$A$ galvanometer of resistance $30 \Omega$ is connected to a battery of emf $2 \text{ V}$ with $1970 \Omega$ resistance in series. $A$ full-scale deflection of $20$ divisions is obtained in the galvanometer. To reduce the deflection to $10$ divisions,the total resistance in series required is: (in $Omega$)

When a current of $5 \ mA$ is passed through a galvanometer having a coil of resistance $15 \ \Omega$,it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range $0 - 10 \ V$ is

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo