A galvanometer coil is replaced by another coil of diameter one-fourth of the original diameter and the total number of turns as ten times the original number. What will be the new deflection if the same current is passed through it?

Answer

`5//8` times the original deflection

Explanation

Case (i), `A_1=piD^2//4, n_1=n, theta_1=theta`
Case (ii) `A_2=pi(D//4)^(2//4)=A_1/16`,
`n_2=10n, theta=?`
`I=(k)/(n_1BA_1)theta_1=(ktheta_2)/(n_2BA_2)`,
so `theta_2=theta_1xx(n_2A_2)/(n_1A_2)=thetaxx10xx1/16=(5theta)/(8)`