Switches and Signals

Closed Switch Path

completing a conducting loop

A closed switch makes a path, so the same circuit laws from DC circuits can determine current. 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 closed switch completes a path

When the switch is closed, the battery, switch, load, and return wire make one conducting loop.

closed switch⇒conducting path\text{closed switch} \Rightarrow \text{conducting path}
Closed switch pathA closed switch completes the loop through the load.12 Vclosed4 ohmA3 A3 A+-12 V

Compute the loop current

The source is 12 volts and the load is 4 ohm, so the closed path carries 3 amperes.

I=VR=12 V4 ohm=3 AI = \frac{V}{R} = \frac{12\ \text{V}}{4\ \text{ohm}} = 3\ \text{A}
Closed switch pathThe ammeter and arrow show the checked current.12 Vclosed4 ohmA3 A3 A+-12 V

Closed paths obey Ohm's law each time

Changing the source and load changes the current, but the rule is still the same closed-loop calculation. The diagram shows the middle row.

VRI6 V3 ohm2 A12 V4 ohm3 A18 V6 ohm3 A\begin{array}{c|c|c}V&R&I\\6\ \text{V}&3\ \text{ohm}&2\ \text{A}\\12\ \text{V}&4\ \text{ohm}&3\ \text{A}\\18\ \text{V}&6\ \text{ohm}&3\ \text{A}\\\end{array}
Closed switch pathThe middle table row is the checked diagram.12 Vclosed4 ohmA3 A3 A+-12 V