A moving-coil galvanometer is shunted by a 2 Ω resistance and then gives full-scale deflection when the total current is 500 mA. In a second arrangement, a 470 Ω resistance is connected in series with the galvanometer and full-scale deflection occurs when 10 V is applied. Find the resistance of the galvanometer coil in ohms.
Physics · Current electricity · electric instruments
JEE Mains 2026 6 April Evening Shift

Question

A moving-coil galvanometer is shunted by a 2 Ω resistance and then gives full-scale deflection when the total current is 500 mA. In a second arrangement, a 470 Ω resistance is connected in series with the galvanometer and full-scale deflection occurs when 10 V is applied. Find the resistance of the galvanometer coil in ohms.

Physics · Current electricity · electric instruments

JEE Mains 2026 6 April Evening Shift

G1 Physics · Accepted Answer

Let the galvanometer resistance be R(G) and the full-scale galvanometer current be I(G). With a 2 Ω shunt and total current 0.5 A, the voltage across the galvanometer and shunt is the same: I(G)R(G) = [0.5-I(G)]×2. Rearrange: I(G)[R(G)+2] = 1, so I(G) = 1 ÷ [R(G)+2]. In the second arrangement, 470 Ω is connected in series and 10 V produces full-scale current: I(G) = 10 ÷ [R(G)+470]. Equate the two expressions: 1 ÷ [R(G)+2] = 10 ÷ [R(G)+470]. Therefore, R(G)+470 = 10R(G)+20. Thus, 450 = 9R(G), R…