Solution:

To construct an ammeter that can read currents up to

$2.0 \, \text{A}$

, we need to calculate the resistance of the shunt. Here's the step-by-step calculation:

1. Full-scale current through the coil:
   The coil takes $1 \, \text{mA} = 10^{-3} \, \text{A}$ 

   for full-scale deflection.

2. Remaining current through the shunt:
   When the total current is $2.0 \, \text{A}$ 

   , the current through the shunt is: 

   $$I_s = I_{\text{total}} - I_c = 2.0 - 10^{-3} = 1.999 \, \text{A}.$$ 

3. Voltage across the coil:
   The resistance of the coil is $25 \, \Omega$ 

   . Using Ohm's law, the voltage across the coil is: 

   $$V_c = I_c R_c = (10^{-3})(25) = 0.025 \, \text{V}.$$ 

4. Resistance of the shunt:
   The voltage across the shunt must equal the voltage across the coil: 

   $$V_s = V_c = 0.025 \, \text{V}.$$Using Ohm's law for the shunt:

    

   $$R_s = \frac{V_s}{I_s} = \frac{0.025}{1.999} \approx 1.25 \times 10^{-2} \, \Omega.$$ 

Thus, the resistance of the shunt is:

$$\boxed{1.25 \times 10^{-2} \, \Omega.}$$