8.5.P30
A model electric system consists of two batteries (labeled B1and B2), three resistors (labeled R1, R2, and R3), and a capacitor (labeled C1), arranged as shown in the figure at the right. All elements and wires are considered ideal.
The batteries each provide a potential rise equal to V0, the resistors have resistance equal to R, and the capacitor has a capacitance equal to C. The circuit is shown at the right with certain locations identified by dots with the letters a through d.
A. On the figures below make a "voltage map". Choose the voltage at point "a" to be 0 and name the voltage at all the corners and junctions in the circuit. If you have some points at which there is a voltage you do not know, give it a new name (e.g., "V1"). If you know that two voltages are the same, give them the same name.
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B. Rank the magnitudes of the currents, Ii across the three resistors (i = 1, 2, 3). Only use greater than (">") or equals ("=") signs.
C. Rank the magnitudes of the voltage drops, ΔVi across the three resistors (i = 1, 2, 3). Only use greater than (">") or equals ("=") signs.
D. write down any equations that you can that expresses relations among the three currents, I1, I2, and I3. Explain briefly below how you know these relations are true.
E. Find the potential drop across the capacitor, expressing your answers in terms of the given parameters of the problem (V0, R, and C). Show your work.
Joe Redish 4/20/18
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