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# Learning Goal: To analyze an RC circuit to determine the initial voltage across a capacitor, the time constant, and the expression for the natural response of the capacitor voltage, and then to find other circuit quantities such as current, voltage, power, or energy. The natural response of an RC circuit is the response of the capacitor voltage to the sudden removal of a DC source. When this occurs, the capacitor releases its stored energy. Part A – Find the initial voltage across the capacitor For the given circuit (Figure 1) , the switch has been at position a for a long time. Find the initial voltage across the capacitor. Assume that. Vg = 45.0V , R1 = 15.0k? , R2 = 7.0k? , R3 = 38.0k?( killo ohm) , and C = 87.0?F (microF) . Express your answer to three significant figures and include the appropriate units. v(0?)=v(0+)Part C – Find an expression for the capacitor voltage, v(t), for t ? 0 (t>=0) Enter an expression for the capacitor voltage v(t) for t?0 . (t>=0) Use the figure in Part B for this part since it shows the circuit after switching. Express your answer as an algebraic expression in terms of R1, R2, R3, Vg, and C. Part D – Find an expression for the current i(t) through resistor R 3 for t ? 0+ (t>=0+) Find an expression for the current i(t) through resistor R3 for t?0+. (t>=0+) Use the figure in Part B for this part since it shows the circuit after switching. Express your answer as a symbolic expression in terms of R1, R2, R3, Vg, and C. Part B – Find the time constant after t = 0 The diagram (Figure 2) represents the original circuit the instant after the switch moves. Find the time constant after t=0. Assume that R1 = 39.0k? , R2 = 12.0k? , R3 = 34.0k? , and C = 85.0?F . Express your answer to three significant figures and include the appropriate units.

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