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Principles and Applications of Electrical Engineering
- 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_forwardDetermine 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 P4.54. a. Write the differential equation for i(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 of the form ip(t)=K exp (−3t). Why doesn’t that work in this case? d. Find the particular solution. [Hint: Try a particular solution of the form ip(t)=K t exp(−3t).] e. Find the complete solution for i(t).arrow_forward
- a. Find the equivalent impedance ZL shown inFigure P4.66(a), as seen by the source, if thefrequency is 377 rad/s.b. If we wanted the source to see the load ascompletely resistive, what value of capacitanceshould we place between the terminals a and b asshown in Figure P4.66(b)? Hint: Find an expressionfor the equivalent impedance ZL, and then find C sothat the phase angle of the impedance is zero.arrow_forwardSolve for i(t) for t>0 in the circuit of Figure P4.67, with R=200 Ω, given that i( 0+ )=0 and v C ( 0+ )=20 V [Hint: Try a particular solution of the form i p ( t )= A cos( 100t )+B sin( 100t ).]arrow_forwardThe circuit shown in Figure P4.39 is operating in steady state with the switch closed prior to t=0. Find expressions for i L ( t ) for t<0 and for t≥0. Sketch iL(t) to scale versus timearrow_forward
- For the circuit shown in Figure P4.38, find an expression for the current i L ( t ) and sketch it to scale versus time. Also, find an expression for vL(t) and sketch it to scale versus timearrow_forwardSubject: control Discuss the effect of adding a pole on the root locus shape , through the relative stability.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_forward
- Solve for the steady-state values of i 1 , i 2 , and i 3 for the circuit shown in FigureP4.21.arrow_forwardConsider the circuit shown in Figure T4.3.a. Write the differential equation for i(t). b. Find the time constant and the form of the complementary solution. c. Find the particular solution. d. Find the complete solution for i(t).arrow_forwardConsider the circuit shown in Figure P4.70. a. Write the differential equation for v(t). b. Find the damping coefficient, the natural frequency, and the form of the complementary solution. c. Usually, for a sinusoidal forcing function, we try a particular solution of the form v p ( t)=A cos( 10 4 t )+B sin( 10 4 t ). Why doesn’t that work in this case? d. Find the particular solution. [Hint: Try a particular solution of the form v p ( t)=At cos( 10 4 t )+B t sin( 10 4 t ). ] e. Find the complete solution for v(t).arrow_forward
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