Consider the circuit shown inFigure P4.49. The voltage source is known as a ramp function, which is defined by
Figure P4.49
Assume that
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Electrical Engineering: Principles & Applications (7th Edition)
- Consider 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_forwardIn the circuit shown in Figure P4.a, the switch is closed at t = 0. The capacitor voltage is charged to vc (0) = 12 V prior to t = 0. The voltage source is us(t) = 35 cos (1000t) V. Find the expressions of uc (t) and ic(t), respectively. vs(t) 500 Ω ww t=0 + v (t) - HH i(t) 1.5 µF 300 Ωarrow_forwardSolve for i L ( t ) for t>0 in the circuit of Figure P4.48. You will need to make an educated guess as to the form of the particular solution. [Hint: The particular solution includes terms with the same functional forms as the terms found in the forcing function and its derivatives.]arrow_forward
- Write the differential equation for i L(t) and find the complete solution for the circuit of Figure P4.45. [Hint: Try a particular solution of the form i Lp ( t )=A e −t .]arrow_forwardSolve for v(t) for t>0 in the circuit of Figure P4.47, given that the inductor current is zero prior to t=0. [Hint: Try a particular solution of the form v p =A cos( 10t )+B sin( 10t ).]arrow_forwardThe switch shown in Figure P4.42 has been closed for a long time prior to t=0, then it opens at t=0 and closes again at t=1s. Find i L (t) for all t.arrow_forward
- 4.5 Write the differential equation for t> 0 for vc in Figure P4.32. t=0 ow R₂ DIO R₁ Figure P4.32 + CVCarrow_forward*P4.61. A dc source is connected to a series RLC circuit by a switch that closes at t = 0, as shown in Figure P4.61. The initial conditions are i(0+) = 0 and vc(0+) = 0. Write the dif- ferential equation for vc(t). Solve for vc(t) given that R = 80 2. t = 0 R 2 mH + V = 50 V i(t) vclt) 5 µF i(0) = 0 vc(0) = 0 Figure P4.61arrow_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_forward
- Write MATLAB program to define the exponentially varying sinusoid f(t) mentioned in topic4.3. Also, include in your code the upper and lower envelopes of f(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_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
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