1. Magnetic field inside a long solenoid

For a long solenoid, $B = \mu_0 n I$ where $n$ is the number of turns per unit length and $I$ is the current through the solenoid.

Since all four solenoids are identical, their magnetic fields are proportional only to the current through them: $B \propto I$

2. Use the given field at solenoid A

At the center of solenoid A, $B_A = 3\text{ T}$ So if current through A is $I_A$, then $\mu_0 n I_A = 3\text{ T}$

3. Find the current relation from the circuit connection

From the given arrangement of four identical solenoids, solenoid $A$ is in one branch while solenoid $C$ carries a smaller current due to the series-parallel combination. For identical resistive solenoids, the current division gives: $I_C = \frac{1}{3} I_A$

Hence, $\frac{B_C}{B_A} = \frac{I_C}{I_A} = \frac{1}{3}$

So, $B_C = \frac{1}{3} \times 3 = 1\text{ T}$

4. Check options

Thus the magnetic field at the center of solenoid $C$ is $\boxed{1\text{ T}}$

So the correct option is D.