Two galvanometers G1 and G_2 are having resistors R1 = 5Ω and R2 = 7Ω, number of turns N1 = 21, N2 = 15

Question

Two galvanomenters \(G_1\) and \(G_2\) are having resistors \(R_1 = 5 \Omega\) and \(R_2 = 7\Omega\), 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 \(A_1 = 3.6 \times 10^{-3}\) and \(A_2 = 1.8 \times 10^{-3} \ cm^3\) . Find the ratio of their voltage sensitivity.

(1) \(\frac{49}{25}\)

(2) \(\frac{7}{5}\)

(3) \(\frac{5}{7}\)

(4) \(\frac{49}{20}\)

Answer 1

Correct option is:  (1) \(\frac{49}{25}\)

\(\tau = NIAB = K \theta\)

\(\frac{\theta}{V} = \frac{\theta}{RI} = \frac{NAB}{LKR}\)

Ratio of voltage sensitivity = \(\left( \frac{N_1 A_1 B_1}{N_2 A_2 B_2} \right) \frac{R_2}{R_1}\)

\(= \frac{21}{15} \times \frac{3.6}{1.8} \times \frac{0.25}{0.50} \times \frac{7}{5} = \frac{49}{25}\)