The error in measuring the current with a tan | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) In a tangent galvanometer,the current $i$ is given by $i = k 	an \phi$,where $k$ is the reduction factor and $\phi$ is the deflection.Differentia

Vedclass · Accepted Answer

$45$

Vedclass · Answer

(C) In a tangent galvanometer,the current $i$ is given by $i = k 	an \phi$,where $k$ is the reduction factor and $\phi$ is the deflection.Differentiating both sides with respect to $\phi$,we get $\frac{di}{d\phi} = k \sec^2 \phi$.Thus,the fractional error is given by $\frac{di}{i} = \frac{k \sec^2 \phi \cdot d\phi}{k 	an \phi} = \frac{d\phi}{\sin \phi \cos \phi}$.Multiplying the numerator and denominator by $2$,we get $\frac{di}{i} = \frac{2 d\phi}{2 \sin \phi \cos \phi} = \frac{2 d\phi}{\sin 2\phi}$.For the error $\frac{di}{i}$ to be minimum,$\sin 2\phi$ must be maximum.The maximum value of $\sin 2\phi$ is $1$,which occurs when $2\phi = 90^o$,or $\phi = 45^o$.

The error in measuring the current with a tangent galvanometer is minimum when the deflection is about $45^o$. (in $^o$)

Similar Questions

When $2 \ A$ current is passed through a tangent galvanometer,it gives a deflection of $30^\circ$. For $60^\circ$ deflection,the current must be........$A$.

$A$ magnetic needle is made to vibrate in a uniform magnetic field $H$. Its time period is $T$. If it vibrates in a field of intensity $4H$,its time period will be:

$A$ vibration magnetometer is placed at the south pole; then its time period will be

$A$ bar magnet of $10 \,cm$ length is kept with its north $(N)$-pole pointing north. $A$ neutral point is formed at a distance of $15 \,cm$ from each pole. Given the horizontal component of Earth's magnetic field is $0.4 \,Gauss$, the pole strength of the magnet is: (in $\,A-m$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module