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AP Physics C: E&M
11.8 Resistor Capacitor (RC) Circuits
11.5 Compound Direct Current Circuits
11.4 Electric Power
IntermediateMCQMathematicalProportional Analysis24.9k
A rectangular circuit schematic drawn in thin black lines on a white background. On the left vertical wire is an ideal battery symbol with long upper plate labeled positive and short lower plate labeled negative, accompanied by the label \(\mathcal{E}\) to its left. The top horizontal wire runs from the battery through a resistor zigzag symbol labeled \(R_1\), then reaches a junction that splits into two vertical parallel branches. The middle vertical branch contains a resistor zigzag symbol labeled \(R_2\). The right vertical branch contains a resistor zigzag symbol labeled \(R_3\) above a parallel-plate capacitor symbol labeled \(C\). Connected in parallel across the capacitor symbol is a bypass loop containing an open single-pole single-throw switch labeled \(S\). The bottom horizontal wire connects the bottoms of the middle branch, right branch, and battery to form a complete closed circuit. No other labels, lines, text, or axes appear.
Circuit with three identical resistors, a capacitor, and a switch.
In the circuit shown, an ideal battery of potential difference \(\mathcal{E}\) is connected in series with a resistor \(R_1\) of resistance \(R\). This combination is connected to two parallel branches: one branch contains resistor \(R_2\) of resistance \(R\), and the other branch contains resistor \(R_3\) of resistance \(R\) in series with a capacitor of capacitance \(C\) that has a switch \(S\) connected in parallel across it. Initially, the switch is closed and the circuit reaches steady state, after which the switch is opened and the circuit reaches a new steady state. What is the ratio of the power dissipated in resistor \(R_2\) in the new steady state to that in the initial steady state, \(\dfrac{P_{\text{new}}}{P_{\text{initial}}}\)?

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