Students investigate a simple series circuit consisting of a 3.0V battery, an ammeter, and a variable resistor clearly marked with a diagonal arrow. The resistance can be set to integer values between 10 Ω and 50 Ω. The students record the current I for three settings and obtain the following data:
Slider setting (Ω): 10, 25, 50
Measured current (mA): 270, 110, 55
Assume the ammeter is ideal and the battery maintains a constant terminal voltage of 3.0V regardless of load.
(a) Describe the qualitative relationship between the resistance of the variable resistor and the current in the circuit as evidenced by the data. Include whether the relationship appears linear, inverse, or of some other form.
(b) Use proportional reasoning based on the given data to estimate the current that would be measured if the resistance were set to 15 Ω. Show all steps in your reasoning and state any assumptions.
(c) The students propose replacing the battery with one that has twice the emf but otherwise identical internal characteristics. Predict how this change would alter the current values across the full range of slider settings. Explain your answer without performing detailed numerical calculations.