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The voltage source shown in Figure P4.51 is called a ramp function Assume that
Figure P4.51
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ANALYSIS+DESIGN OF LINEAR CIRCUITS(LL)
- We know that the capacitor shown in Figure P4.11 is charged to a voltage of 10 V priorto t=0.a. Find expressions for the voltage across the capacitor vC(t) and the voltage across theresistor vR(t) for all time.b. Find an expression for the power delivered to the resistor.c. Integrate the power from t=0 to t=∞ to find the energy delivered.d. Show that the energy delivered to the resistor is equal to the energy stored in thecapacitor prior to t=0.arrow_forwardConsider the circuit of Figure P4.17, in which the switch instantaneously moves back and forth between contacts A and B, spending 2 seconds in each position. Thus, the capacitor repeatedly charges for 2 seconds and then discharges for 2 seconds. Assume that v C ( 0 )=0 and that the switch moves to position A at t=0. Determine v C ( 2 ), v C ( 4 ), v C ( 6 ), and v C ( 8 ).arrow_forwardThe capacitor model we have used so far has beentreated as an ideal circuit element. A more accuratemodel for a capacitor is shown in Figure P4.67. Theideal capacitor, C, has a large “leakage” resistance, RC,in parallel with it. RC models the leakage currentthrough the capacitor. R1 and R2 represent the leadwire resistances, and L1 and L2 represent the lead wireinductances.a. If C = 1 μF, RC = 100 MΩ, R1 = R2 = 1 μΩ andL1 = L2 = 0.1 μH, find the equivalent impedanceseen at the terminals a and b as a function offrequency ω.b. Find the range of frequencies for which Zab iscapacitive, i.e., Xab > 10|Rab.Hint: Assume that RC is is much greater than 1/wC so thatyou can replace RC by an infinite resistance in part b.arrow_forward
- Consider the circuit shown in Figure P4.55. a. Write the differential equation for v(t).b. Find the time constant and the form of the complementary solution.c. Usually, for an exponential forcing function like this, we would try a particular solution ofthe form vp(t) = K exp (−10t). Why doesn’t that work in this case?d. Find the particular solution. [Hint: Try a particular solution of the form vp(t)=K t exp (−10t). How ]e. Find the complete solution for v(t).arrow_forwardUse the defining law for a capacitor to find the current iC(t) corresponding to the voltage shown in Figure P4.27. Sketch your result.arrow_forwardConsider the circuit shown in Figure T4.4 in which the initial inductor current and capacitor voltage are both zero. a. Write the differential equation for v C (t). b. Find the particular solution. c. Is this circuit overdamped, critically damped, or underdamped? Find the form of the complementary solution. d. Find the complete solution for v C (t).arrow_forward
- Determine expressions for and sketch i s ( t ) to scale versus time for −0.2≤t≤1.0 s for the circuit of Figure P4.37.arrow_forwardConsider the circuit shown in Figure P4.50. The initial current in the inductor is i s ( 0+)=0. Write the differential equation for i s(t) and solve. [Hint: Try a particular solution of the form i sp ( t )=A cos( 300t )+B sin( 300t ).]arrow_forwardFor the circuit shown in Figure P4.29, the switch is closed for a long time prior to t=0.Find expressions for vC(t) and sketch it to scale for −80≤t≤160 ms.arrow_forward
- The current waveform shown in Figure P4.23 flowsthrough a 2-H inductor. Plot the inductor voltage vL(t).arrow_forwardThe circuit shown in Figure P4.26 is operating in steady state. Determine the values of i L,v x ,and v C .arrow_forwardThe initial voltage across the capacitor shown in Figure P4.3 is v C ( 0+ )=0. Find an expression for the voltage across the capacitor as a function of time, and sketch to scale versus timearrow_forward
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