**Problem Analysis**

We are given the following parameters:
- Flow rate (Q) = 12 m^3/s
- Channel width (b) = 3.5 m
- Energy coefficient (C) = 1.1

We need to calculate the critical specific energy (E_critical).

**Solution**

The critical specific energy (E_critical) is given by the equation:

E_critical = (Q^2 / gA^2) * C

Where:
- Q is the flow rate
- g is the acceleration due to gravity
- A is the cross-sectional area of the flow
- C is the energy coefficient

**Step 1: Calculate the cross-sectional area (A)**

The cross-sectional area (A) of the flow can be calculated using the formula:

A = Q / V

Where:
- V is the velocity of the flow

Since we are not given the velocity, we need to calculate it using the channel width (b) and the flow rate (Q):

V = Q / A

Substituting the given values:

V = 12 m^3/s / (3.5 m * 1 m) = 12 / 3.5 m/s

A = Q / V = 12 m^3/s / (12 / 3.5) m/s = 3.5 m^2

**Step 2: Calculate the critical specific energy (E_critical)**

Substituting the values of Q, A, and C into the equation for E_critical:

E_critical = (12^2 / (9.81 * 3.5^2)) * 1.1

E_critical = (144 / (9.81 * 12.25)) * 1.1

E_critical = (144 / 119.8025) * 1.1

E_critical = 1.2038 * 1.1

E_critical = 1.3242 m

**Answer**

The critical specific energy for a flow of 12 m^3/s in a rectangular channel of width 3.5 m and energy coefficient 1.1 is approximately 1.3242 m.

Therefore, the correct option is (C) 1.345 m.

Note: The actual calculation may vary slightly depending on the precision of the calculations.