AP Physics 1 Question 415: Answer and Explanation
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3. Two resistors, R1 and R2, have equal resistance, and are connected in a circuit with a battery as shown in the figure above. If a third resistor, also with the same resistance, is then connected to the circuit, as shown, what happens to the energy E1 and E2 dissipated by R1 and R2, respectively, during a given time interval?
- A. E1 and E2 both decrease.
- B. E1 remains constant while E2 decreases.
- C. E1 decreases while E2 remains constant.
- D. E1 and E2 both remain constant.
Correct Answer: D
Kirchhoff's Loop Law can be applied to the loop containing only the battery and R1 and separately to the loop containing only the battery and R2 to show that ΔV1 = ΔV2 = Vbat. This is true with or without the addition of R3. Since I = ΔV/R and the voltages across R1 and R2 do not change with the addition of R3, the current through each of the resistors also doesn't change. If the current through and the voltage across both R1 and R2 remain constant, the energy dissipated by each resistor per unit time also remains constant.