Electric current is measured by a tangent gal | vedclass

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Question

(B) Given that the current $I \propto 	an 	heta$. Taking the derivative with respect to $	heta$,we get $dI = k \sec^2 	heta \, d	heta$. Dividing

Vedclass · Accepted Answer

$\frac{\pi}{2} \%$

Vedclass · Answer

(B) Given that the current $I \propto 	an 	heta$. Taking the derivative with respect to $	heta$,we get $dI = k \sec^2 	heta \, d	heta$. Dividing by $I = k 	an 	heta$,we have $\frac{dI}{I} = \frac{\sec^2 	heta}{	an 	heta} d	heta = \frac{1}{\sin 	heta \cos 	heta} d	heta = \frac{2}{\sin(2	heta)} d	heta$. Given $	heta = 45^{\circ} = \frac{\pi}{4}$ radians,and the error in reading $	heta$ is $1 \%$,so $d	heta = \frac{1}{100} 	imes \frac{\pi}{4} = \frac{\pi}{400}$ radians. Substituting these values: $\frac{dI}{I} = \frac{2}{\sin(90^{\circ})} 	imes \frac{\pi}{400} = 2 	imes 1 	imes \frac{\pi}{400} = \frac{\pi}{200}$. To find the percentage error: $\frac{dI}{I} 	imes 100 = \frac{\pi}{200} 	imes 100 = \frac{\pi}{2} \%$. Therefore,the correct option is $(b)$.

Electric current is measured by a tangent galvanometer,where the current is proportional to the tangent of the angle $\theta$ of deflection. If the deflection is read as $45^{\circ}$ and an error of $1 \%$ is made in reading it,then the percentage error in the current is:

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