Threshold Control Three-Row Scan - Electronic Circuits III: Comparators and Interfaces Step by Step

A controlled switch is trusted only after the below, boundary, and above-threshold rows are all visible. 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 controlled switch needs rows around the boundary

The source and load stay fixed while the control input is scanned below, at, and above the threshold. That makes the boundary a displayed row, not a hidden assumption.

V_c>V_{\text{th}}\Rightarrow\text{closed}

Three control values expose the strict decision

Only the last row closes. The two earlier rows carry zero load current because this ideal controlled switch uses a strict greater-than rule.

\begin{array}{c|c|c|c}V_c&V_{\text{th}}&\text{state}&I_L\\4\ \text{V}&5\ \text{V}&\text{open}&0\ \text{A}\\5\ \text{V}&5\ \text{V}&\text{open}&0\ \text{A}\\6\ \text{V}&5\ \text{V}&\text{closed}&3\ \text{A}\\\end{array}

The above-threshold row returns to Ohm's law

When the control reaches 6 volts, the switch closes and the load current is 3 amperes.

12\ \text{V}/4\ \text{ohm}=3\ \text{A}

The scan separates decision logic from load arithmetic

The table first decides whether the path exists. Only the closed row then uses the battery and load resistance to compute current.

5\ \text{V}=5\ \text{V}\Rightarrow I_L=0\ \text{A}