We have to be a little careful working with this question. Do you mean
that current is "constant" or do you mean it's "the same current" ?
-- If the energy source for the circuit is supplying DC ... like a battery
or a solar cell ... then the current is 'constant' at every point in the
circuit. It's not changing. It's the same now as it was 10 seconds
ago. But it's NOT necessarily the same amount of current everywhere
in the circuit.
-- If the energy source for the circuit is not supplying DC ... if it's an
AC generator, or a charged capacitor, or a function generator ...
then wherever you look in the circuit, the current is constantly
changing its value at that point.
-- And if there's any place in the circuit where there are components
connected in parallel, then the current must have different values
at different points in the circuit.
It can't be the same current everywhere.
