AP Physics 2 Free Response #1 (Unit 04) Electric Circuits

This is a publicly released AP Physics 2 free response question dealing with content from Unit 4, Electric Circuits. This question deals with the graphical relationship between current and potential difference for "ohmic" resistors, Kirchhoff's Loop Rule, solving for the equivalent resistance of a complex circuit, and using Ohm's Law to solve for the voltage across resistor and the current which flows through different resistors.

"The two circuits shown above contain an ideal variable power supply, an ohmic resistor of resistance R, an ammeter A, and two voltmeters VPS and VR . In circuit 1the ammeter has negligible resistance, and in circuit 2 the ammeter has significant internal ohmic resistance r . The potential difference of the power supply is varied, and measurements of current and potential difference are recorded.

(a) The axes below can be used to graph the current measured by the ammeter as a function of the potential difference measured across the power supply. On the axes, do the following.

Sketch a possible graph for circuit 1 and label it 1.
Sketch a possible graph for circuit 2 and label it 2.

(b) Let ΔVPS be the potential difference measured by voltmeter VPS across the power supply, and let I be the current measured by the ammeter A. For each circuit, write an equation that satisfies conservation of energy, in terms of ΔVPS, I, R, and r, as appropriate.

(c) Explain how your equations in part (b) account for any differences between graphs 1 and 2 in part (a).

(d) In circuit 2, R=40Ω. When voltmeter VPS reads 3.0V, voltmeter VR reads 2.5V. Calculate the internal resistance r of the ammeter.

(e) Voltmeter VR in circuit 2 is replaced by a resistor with resistance 120Ω to create circuit 3 shown below. Voltmeter VPS still reads 3.0V.

i. Calculate the equivalent resistance Req of the circuit.
ii. Calculate the current in each of the resistors that are in parallel."