Closed Switch Path - Electricity and Electronic Circuits Step by Step

A closed-switch-path scan treats the closed switch as a perfect conductor and varies the source voltage and load resistance across three rows, checking that the loop current I = V / R recomputes row by row. The arithmetic is exact only for the stated source voltages, load resistances, currents, and rows in the ideal switch, supply, and load model. Real circuits add contact resistance, leakage, finite rise time, supply tolerance, load impedance, probe/calibration limits, finite precision, and measurement uncertainty.

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.

\text{closed switch} \Rightarrow \text{conducting path}

Compute the loop current

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

I = \frac{V}{R} = \frac{12\ \text{V}}{4\ \text{ohm}} = 3\ \text{A}

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.

\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}