A galvanometer possessing a coil of resistance $80 \Omega$ displays full-scale deflection when a cur

Question

A galvanometer possessing a coil of resistance $80 \Omega$ displays full-scale deflection when a current of $2.0 \mathrm{~A}$ passes through it. It can be systematically converted into an ammeter to read currents up to $10.0 \mathrm{~A}$ by

Professor PC Thomas Classes · Answer

(c) : The galvanometer requires $I_g = 2.0 \mathrm{~A}$ for full-scale deflection and has a resistance of $G = 80 \Omega$. To measure a total current of $I = 10.0 \mathrm{~A}$, a shunt resistance $S$ must be placed in parallel so that the excess current ($I - I_g$) bypasses the galvanometer. The potential drop across the parallel branches must be equal: $I_g G = (I - I_g) S$. Substituting the values: $2.0 	imes 80 = (10.0 - 2.0) 	imes S \implies 160 = 8.0 	imes S$. Thus, $S = \frac{160}{8} = 20 \Omega$. A $20 \Omega$ resistor must be connected in parallel.