Charge, Current, and Voltage

Current in a Loop

one path, one current

In a single loop the current is the same everywhere, because charge cannot build up or vanish. What goes round comes round.

Example

In a single loop the current is the same everywhere, because charge cannot build up or vanish. What goes round comes round. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A loop has only one path

Look at this single loop. There is exactly one path around it: through the battery, along the top, through the ammeter, through the resistor, and back along the bottom. There is nowhere to branch off.

one loop⇒one path for charge\text{one loop} \Rightarrow \text{one path for charge}
One loop, one currentA single loop with a battery, an ammeter, and a resistor; arrows mark the current on each side and all read the same amount.A3 AR3 A3 A3 A

Charge cannot build up

The wire does not collect charge: any charge that flows in at one end of a piece of wire must flow out at the other, or the wire would pile up charge and stop the current. So the flow rate must be the same through every piece.

Ibattery=Iwire=IresistorI_{\text{battery}} = I_{\text{wire}} = I_{\text{resistor}}

Different loops may differ; one loop must match

A different battery-and-resistor pair could make a different current, but within any one single loop the readings still match. The table scans three possible loops: each row may change, but the three places in that row stay equal.

IleftItopIright1 A1 A1 A2 A2 A2 A3 A3 A3 A\begin{array}{c|c|c}I_{\text{left}} & I_{\text{top}} & I_{\text{right}} \\1\ \text{A} & 1\ \text{A} & 1\ \text{A} \\2\ \text{A} & 2\ \text{A} & 2\ \text{A} \\3\ \text{A} & 3\ \text{A} & 3\ \text{A}\end{array}
One loop, one currentA single loop with a battery, an ammeter, and a resistor; arrows mark the current on each side and all read the same amount.A3 AR3 A3 A3 A

Every reading is the same

The ammeter in the top wire reads 3 amperes. Because the current cannot be different anywhere in a single loop, the arrows on the other sides also read 3 amperes. That is charge-flow conservation: what goes round, comes round.

I=3 A    everywhere in the loopI = \hl{3}\ \text{A} \;\; \text{everywhere in the loop}
One loop, one currentA single loop with a battery, an ammeter, and a resistor; arrows mark the current on each side and all read the same amount.A3 AR3 A3 A3 A
electricity The ammeter reads 3 A and so does every current arrow around the one loop: with only one path there is nowhere for charge to branch off. Why it is 3 A at all is Ohm's law, the next chapter.