A capacitor C1 =1F is connected to a 1V battery using a wirewith a total resistance R = 1Ohm
Suppose after the charging is complete the capacitor C1 isconnected to another capacitor C2 = 2 F using a wire with a totalresistance of R =0.3 Ohm. Now the first capacitor discharges whilethe second one charges.
2.8 [1pt] How much charge was transferred through the resistor Rduring the discharge?
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2.9 [1pt] How much energy was dissipated in the resistor Rduring the discharge
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Let’s derive the differential equation describing the dischargein this 2-capacitor circuit. Let’s label the charge on thecapacitor C1 as q1(t) and the charge on the capacitor C2 asq2(t).
2.10 [1pt] Sketch the circuit diagram, label the charges andtheir signs at the capacitors plate, and link q1(t) and q2(t).
Hint, what is q1(t=0) and q2(t=0) (t=0 is the instant theconnection was made)?
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2.11 [1pt] Express the current through the resistor in terms ofthe charge derivative and write down the voltages across bothcapacitors and the resistor add up to zero. From the resultingequation, deduce the characteristic charging time without solvingit.
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