Galvanometer To Ammeter

Converting a galvanometer into an ammeter requires a low-resistance shunt placed in parallel, so most of the current bypasses the sensitive coil while only its full-scale current passes through it. The shunt satisfies (I_g G = (I - I_g) S), where (I_g) is the galvanometer's full-scale current, (G) its resistance, (I) the desired range, and (S) the shunt. Here (I_g = 4 \times 10^{-3}) A, (G = 50;\Omega), and (I = 2) A, so (S = \frac{I_g G}{I - I_g} = \frac{4 \times 10^{-3} \times 50}{2 - 0.004} = \frac{0.2}{1.996} \approx 0.1;\Omega). The value 0.5 (\Omega) overestimates by omitting the large range current in the denominator. The value 1.0 (\Omega) misplaces a power of ten in (I_g). The value 0.2 (\Omega) forgets to divide by the bypass current. This is the NCERT shunt formula for ammeter conversion. A plausibility check confirms it: since the shunt must divert nearly all of the 2 A around a 50 (\Omega) coil carrying just 4 mA, it must be extremely small, consistent with about 0.1 (\Omega). This also explains why an ideal ammeter is taken to have nearly zero resistance: connected in series, it must not add appreciable opposition to the branch it measures, and the parallel shunt achieves exactly this by keeping the overall meter resistance far below that of the circuit it is inserted into.