Question

Two galvanometers \(G_1\) and \(G_2\) are having resistors \(R_1 = 5W\) and \(R_2 = 7W\), number of turns \(N_1 = 21,\ N_2 = 15\), magnetic fields \(B_1 = 0.25\ T,\ B_2 = 0.50\ T\) and area of coil \(A_1 = 3.6\times 10^{-3} \ cm^2\) and \(A_2 = 1.8\times 10^{-3}\ cm^2\). Find the ratio of their voltage sensitivity (same spring in both)

(1) \(\frac{5}{7}\)

(2) \(\frac{49}{20}\)

(3) \(\frac{49}{25}\)

(4) \(\frac{7}{5}\)

Answer 1

Correct option is : (3) \(\frac{49}{25}\) 

Voltage sensitivity = \(\frac{NAB}{CR}\)

\(\frac{\chi_1}{\chi_2} = \frac{N_1}{N_2} \times \frac{A_1}{A_2} \times \frac{B_1}{B_2} \times \frac{R_2}{R_1}\)

\( = \frac{21}{15} \times \frac{36}{18} \times \frac{0.25}{0.5} \times \frac{7}{5} = \frac{49}{25}\)