Two moving coil galvanometer, X and Y have coils with resistance 10 and 14 cross-sectional areas 4.8 10⁻³ ~m ^2 and 2.4 10⁻³ ~m ^2 , number of turns 30 and 45 respectively. They are placed in magnetic field of 0.25 ~T and 0.50 ~T respectively. Then, the ratio of their current sensitivities and the ratio of their voltage sensitivities are respectively

Step-by-step solution

There is no information regarding spring constant. So, let's assume their spring constants are same. Current sensitivity, I_S= N B A k So, aligned I_ S₁ I_ S₂ & = N₁ B₁ A₁ k₂ N₂ B₂ A₂ k₁ & = 30 0.25 4.8 10⁻³ 45 0.5 24 10⁻³ ( 1 1 ) I_ S₁ I_ S₂ & =2 / 3 aligned Voltage sensitivity, V_S=N B A / R k So, aligned V_ S₁ V_ S₂ & = N₁ B₁ A₁ k₂ R₂ N₂ B₂ A₂ k₁ R₁ & = 2 3 ( R₂ R₁ )= 2 3 14 10 = 14 15 aligned