Design Challenge
A research team needs a portable diagnostic circuit that can perform three functions simultaneously when connected to a single unknown resistor sample:
1. Illuminate an indicator lamp whenever current flows through the sample.
2. Measure the instantaneous current through the sample without significantly altering that current.
3. Measure the potential difference across the sample without drawing appreciable additional current through it.
The team has access only to the following ideal components, each represented by its standard schematic symbol: a 9V battery, conducting wire, a lightbulb (modeled as a resistor that produces visible light at 20mA), a standard single-pole switch, an ammeter, and a voltmeter.
Answer the following questions.
(1) Construct a complete schematic diagram that fulfills all three functional requirements listed above. Your diagram should indicate clearly where the switch, ammeter, voltmeter, lamp, battery, and sample resistor are placed.
(2) Justify the series or parallel placement of each measuring device with respect to the sample resistor. Include in your justification how each meter’s internal resistance relates to its intended function and why its placement avoids altering the quantity it measures.
(3) Suppose the team accidentally wires the voltmeter in series with the sample resistor instead of in parallel. Derive an expression for the current that would flow through the sample in that erroneous configuration in terms of the battery voltage Vb, the sample resistance Rs, and the voltmeter’s internal resistance Rv. Discuss the operational consequences for the lamp and the accuracy of both current and voltage measurements.
(4) Propose one modification to your original design that would allow the team to add a second indicator lamp that lights only when the measured potential difference across the sample exceeds 5V. Explain how your modification achieves this threshold behavior using only ideal circuit elements permitted in the problem.