Transistor as Switch - Electronic Circuits II & III: Decision Networks and Interfaces Step by Step

A transistor-as-switch scan treats the transistor as an ideal controlled switch, checking the control voltage against a threshold and then closing the load path at I = V / R when control exceeds threshold. The arithmetic is exact only for the stated control voltages, threshold voltages, source voltages, load resistances, currents, switch states, and rows in the ideal controlled-switch model. Real transistor switches add saturation voltage, leakage, gain spread, resistor tolerance, input threshold variation, probe/calibration limits, finite precision, and measurement uncertainty.

A transistor can be used as an ideal controlled switch when the book explicitly defers device curves and gain. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The control voltage is checked against threshold

The control is 5 volts and the threshold is 3 volts, so the ideal switch is closed.

5\ \text{V} > 3\ \text{V}

A closed path sets the load current

With a 12 volt source and a 4 ohm load, the checked current is 3 amperes. This is only an ideal switch model; transistor gain and bias are deferred.

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