Your model is going to be the same, whatever is the length of your input.
In Torch we used to clone the model as many times as the time steps while sharing the parameters, because it is the same model, just over time.
The number of parameters will change when your input dimensionality will change (the size of x[t], for a given t = 1, ..., T), and not when T changes.
If it is still not clear, you can go over my lectures on RNNs (ref. 99).
And if it is still confusing, wait for the PyTorch video tutorials I’m currently working on.