AP Physics 2 FRQ: Adding a bulb in parallel

Qualitative/Quantitative Translation, 8 pointsAbout 21 minutes · 8 points

A battery of emf ε and negligible internal resistance is connected in series with two identical lightbulbs, A and B, as shown. A third identical bulb, C, is connected in parallel with bulb B through a switch S, which is initially open. Each bulb has a resistance R that does not change, and a bulb glows more brightly when it dissipates more power. The switch is then closed.

(A) A student claims: "Closing the switch adds another bulb, so the battery's energy is shared among more bulbs, and every bulb that was already lit becomes dimmer." Indicate whether the student's claim is correct for bulb A and whether it is correct for bulb B. In a clear, coherent, paragraph-length response that may also contain equations, justify your answers by reasoning about the currents and potential differences in the circuit. Do not derive expressions for the power in this part. 3 points

(B) Derive expressions for the power

P_{\mathrm{A}}

dissipated by bulb A and the power

P_{\mathrm{B}}

dissipated by bulb B after the switch is closed, in terms of ε and R. Begin your derivation by writing a fundamental principle or an equation from the reference information. 3 points

(C) Before the switch is closed, bulbs A and B each dissipate a power of ε²/(4R). Explain whether your expressions in part B are consistent with your answers in part A. 2 points