Why does amperage stay the same in a circuit?

Answer 1

Amperes represents a flow of charge (coulombs) in a circuit in a period of time (seconds). In order to have that flow, you have to have conductance, which is the inverse of resistance. Since the conductance of two circuits not connected to each other is zero (infinite resistance, neglecting leakage) there can be no current flow between disjoint circuits. A node is a junction between two elements in a circuit, such as the connection between a resistor and a light bulb. If you consider that the only circuit between those two elements contains that node, and that leakage is inconsequential in comparision to the conductance of the circuit, then you have to note that the current entering the node must be the same as the current leaving the node. In fact, this is Kirchoff's Current Law: The sum of the currents entering a node must equal the sum of the currents leaving a node. (Usually, we think of current entering to be one sign (+) and current leaving to be the other sign (-), so the sum of all currents relative to the node is zero.) Expand this thinking little by little to encompass the elements in the circuit. Again, there is no path for current to flow other than through the elements of the circuit. This means that the current in every part of the circuit is the same. Keep in mind that this applies only to series circuits. In a parallel circuit, current can branch out between two elements connected to a node supplied by another element. In that case, the current in each branch will be different, depending on the resistance and voltage of that path. Circuit analysis is simply the consolidation of a complex circuit into a simple circuit by repeated application of various conversions, such as Norton and Thevanin equivalents, with the ultimate goal of knowing the voltage, current, and resistance for each element.

Answer 2

It doesn't. Current is related to Voltage by Ohms law: V=IR.

However, it would be possible if R the resistance changes too.