ECE2040D_HW6_Soln

ECE2040D_HW6_Soln - ECE 2040D Solutions to HW#6 - Spring...

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P8.3-3 Before the switch closes: After the switch closes: Therefore g G 6 3 so 3 0.05 0.15 s 2 t R ± ² ³ ³ ´ ³ ³ ² . Finally, 6.67 ( ) ( (0) ) 6 18 V for 0 t t oc oc v v v e e t ² ² ³ µ ² ³ ² µ v t P8.3-4 Before the switch closes: After the switch closes: ECE 2040D Solutions to HW#6 - Spring 2009 Page 1 / 11
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Therefore 6 6 3 so 2 2 3 t R g G ± ± ² ± ± G s . Finally, 0.5 10 ( ) ( (0) ) 2 A for 0 3 t t sc sc i i i e e t G G ± ³ G ± G ³ ´ i t P8.3-5 Before the switch opens, µ ¶ µ ¶ 0 V 0 0 V o o v t v ± · ± . After the switch opens the part of the circuit connected to the capacitor can be replaced by it's Thevenin equivalent circuit to get: Therefore . µ ¶µ ¶ 3 6 20 10 4 10 0.08 s G ± ¸ ¸ ± Next, 12.5 ( ) ( (0) ) 10 10 V for 0 t t C oc oc v v v e e t G G ± ³ G ± G ´ v t 12.5 0 t C G Finally , v t ( ) ± ± v ( t ) 10 G 10 e V for t ´ 0 ECE 2040D Solutions to HW#6 - Spring 2009 Page 2 / 11
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P8.3-8 Before the switch opens, the circuit will be at steady state. Because the only input to this circuit is the constant voltage of the voltage source, all of the element currents and voltages, including the capacitor voltage, will have constant values. Closing the switch disturbs the circuit by shorting out resistor R . Eventually the disturbance dies out and the circuit is again at steady state. All the element currents and voltages will again have constant values, but probably different constant values than they had before the switch closed. Here is the circuit before t = 0, when the switch is closed and the circuit is at steady state. The closed switch is modeled as a short circuit. The combination of resistor and a short circuit connected is equivalent to a short circuit. Consequently, a short circuit replaces the switch and the resistor R . A capacitor in a steady-state dc circuit acts like an open circuit, so an open circuit replaces the capacitor. The voltage across that open circuit is the capacitor voltage, v o ( t ). Because the circuit is at steady state, the value of the capacitor voltage will be constant. This constant is the value of the capacitor voltage just before the switch opens. In the absence of unbounded currents, the voltage of a capacitor must be continuous. The value of the capacitor voltage immediately after the switch opens is equal to the value immediately before the switch opens. This value is called the initial condition of the capacitor and has been labeled as v o (0). There is no current in the horizontal resistor due to the open circuit. Consequently, v o (0) is equal to the voltage across the vertical resistor, which is equal to the voltage source voltage. Therefore g G o s 0 v V ± The value of v o (0) can also be obtained by setting t = 0 in the equation for v o ( t ). Doing so gives
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ECE2040D_HW6_Soln - ECE 2040D Solutions to HW#6 - Spring...

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