Electric Power AP Physics 2 FRQ

Question 

(12 points, suggested time 25 minutes)
A circuit consists of an ideal battery of emf Ɛ and four identical resistors \(R_{1}\) , \(R_{2}\), \(R_{3}\), and \(R_{4}\), each of resistance R, as shown in Figure 1.
(a) For parts (a)(i) and (a)(ii), express your answers in terms of numerical values, Ɛ, and R only.

i. Derive an expression for the current \(I_{1}\) in Resistor \(R_{1}\).

ii. Derive an expression for the current \(I_{3}\) in Resistor \(R_{3}\).

(b) The partially completed bar chart in Figure 2 shows a bar that represents the absolute value \(\left| \Delta V\right|\) of the potential difference across the ideal battery.

• In Figure 2, draw a bar to represent \(\left| \Delta V\right|\) across each resistor, relative to the emf Ɛ of the ideal battery.
• The height of each bar should be proportional to the value of  \(\left| \Delta V\right|\) represented by that bar. If  \(\left| \Delta V\right|\)  is zero, write a “0” in that column

A student claims that the rate at which energy is dissipated (power) by the circuit can be expressed as \(p = \frac{3\varepsilon ^{2}}{5R}\)

(c) State whether the expression for P is correct or incorrect. Justify your answer by referring to the derivations from part (a) or the bar chart from part (b).

When the ideal battery is connected in the original circuit, the rate at which energy is dissipated by Resistor \(R_{1}\) is \(P_{original}\). The ideal battery is now replaced with a nonideal battery of emf Ɛ and internal resistance r to form the new circuit shown in Figure 3. The rate at which energy is dissipated by Resistor \(R_{1}\) in the new circuit is \(P_{new}\).

(d) Indicate whether \(P_{new}\) is greater than, less than, or equal to \(P_{original}\).
_____ \(P_{new}\)> \(P_{original}\)_____ \(P_{new}\) < \(P_{original}\) _____ \(P_{new}\) = \(P_{original}\)
Briefly justify your answer