1. Model the Circuit:
We can model the unknown network between terminals A and B as a Thevenin equivalent circuit with voltage V_th and series resistance R_th.

2. Case 1: Ideal Ammeter (Short Circuit):
An ideal ammeter has zero resistance.
I = V_th / R_th = 4 A    … (Equation 1)

3. Case 2: With 3Ω Resistor:
When a 3Ω resistor is added in series, the total resistance is R_th + 3.
I = V_th / (R_th + 3) = 2 A    … (Equation 2)

4. Solve the System:
From Eq 1, V_th = 4 R_th. Substitute this into Eq 2:
4 R_th / (R_th + 3) = 2
4 R_th = 2 R_th + 6
2 R_th = 6 &implies; R_th = 3 Ω

5. Find Thevenin Voltage:
V_th = 4 × 3 = 12 V

An ideal voltmeter connected to A and B measures the open-circuit voltage, which is exactly V_th.