Measuring Current and Potential Difference

Current is the flow of charge past a point, so to measure it you have to get in the way of that flow and count it as it passes through. That's why an ammeter is wired in series: it becomes part of the path, and every electron bound for the component must first go through the meter. For this to work without lying to you, an ideal ammeter has zero resistance, so inserting it changes nothing about the circuit's behavior. Voltage, by contrast, is a comparison between two points, a difference in electric potential energy per charge. You don't need to interrupt the flow to compare two points, you just need to touch both of them, so a voltmeter connects in parallel across a component. An ideal voltmeter has infinite resistance, so the tiny bit of circuit it bridges carries no current and steals nothing from the real path.

Real meters fall short of these ideals, and the mismatch matters most in opposite situations. A real ammeter has some small resistance, which matters most when it's placed in a low-resistance circuit, since that resistance becomes a bigger fraction of the total. A real voltmeter has large but finite resistance, which matters most across a very large resistor, since the voltmeter's path can then carry a current close in size to the original one, pulling down the voltage it's trying to read. Both errors come from the same idea: any real meter is itself a circuit element, and it only measures faithfully when its own effect is negligible next to what it's measuring. This connects directly to the series and parallel resistance rules from earlier: adding a low-resistance ammeter in series raises total resistance slightly, while adding a finite-resistance voltmeter in parallel creates a new current path that lowers the equivalent resistance seen by the rest of the circuit.