In an ammeter, 0.2 of the main current passes through the galvanometer.

Let i be the main current. In an ammeter, 0.2 of the main current passes through the galvanometer (G). Therefore, the current through the galvanometer is 0.2i = iG. The remaining current (i - 0.2i = 0.8i) passes through the shunt (S). Since the galvanometer (G) and the shunt (S) are in parallel combination, the voltage across them is the same.

Therefore, we have:

iG * G = iS * S
(0.2i)G = (0.8i)S

Solving for the ratio of S to G:

0.2G = 0.8S
S/G = 0.2/0.8 = 1/4

The equivalent resistance of the ammeter (Req) is given by the parallel combination of G and S:

1/Req = 1/G + 1/S

If we assume that the shunt resistance is 1/4 the value of the galvanometer resistance, and the current through the galvanometer is 0.2 of the main current then we can calculate the correct value. We know that i_g = 0.2i_main and V_g = V_s (since they are parallel). Using ohms law, 0.2i_mainG = 0.8i_mainS. Therefore, S = 0.2G/0.8 = G/4. If G = 1, then S = 0.25. Therefore 1/Req = 1/1 + 1/0.25 = 5, Req = 0.2. This doesn't match the options provided directly. However, the provided solution seems to imply that the galvanometer resistance (G) is given and uses a different approach to find the shunt resistance (S). Let's examine the given solution:

The solution states: iG * G = iS * S => (0.2i)G = (0.8i)S => S = G/4
This means that the shunt resistance S is one-fourth the resistance of the galvanometer G. Let's look at the given options:

• 500/499G: This ratio is approximately 1. The ratio between shunt and galvanometer resistance is 1/4, so this option is incorrect.
• 499/500G: This ratio is approximately 1. The ratio between shunt and galvanometer resistance is 1/4, so this option is incorrect.
• 1499G: The given solution doesn't explicitly lead to this value.
• 1500G: The given solution doesn't explicitly lead to this value.

The provided solution is incomplete and lacks clarity in relating the equations to the provided options. The numerical values in the solution, like 500 and 499, seem arbitrary and are not clearly explained. The complete and correct derivation would need additional information or clarification regarding the context and specific values used.