1- Find the complete response v(t) for t > 0. Circuit is at steady state at t = 0. Show the complete work. (50 pts) L = 0.54 H C = 0.185 F Hint: Roots of characteristic equation: $s_1 = -1$ and $s_2 = -4$ $v_s = 10e^{-5t}u(t) V$ $i_L$ $i_c$ $r = 0$ 4 ? a +16 V + 6 ?
Added by Connie G.
Close
Step 1
We are given the roots of the characteristic equation as C = 0.185 F and L = 0.54 H. The characteristic equation for an RL circuit is given by: s^2 + (R/L)s + (1/LC) = 0 Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 86 other Physics 102 Electricity and Magnetism educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
For the following circuit: a. Find ̑. b. Find ̑₀. c. Write a differential equation in v(t). d. Find the characteristic equation. e. Find the roots of the characteristic equation. f. Find the final value of voltage v(t) across the capacitor. g. Find voltage v(t) across the capacitor for t ≥ 0 and plot v(t). h. Find current i(t) for t ≥ 0 and plot i(t). R = 4 k̑ L = 10 mH I₀ = 6 mA C = 2.5 nF V₀ = 4 V
Sri K.
Find the transient current (a general solution) in the $R L C$ -circuit in Fig. 60 for the given dats. (Show the details of your work.) $$\begin{array}{l} R=1 / 10 \Omega, L=1 / 2 \mathrm{H}, C=100 / 13 \mathrm{F} \\ E=e^{-4\left(1.932 \cos \frac{1}{2} t+0.246 \sin \frac{21}{2} r\right)} \mathrm{V} \end{array}$$
Second-Order Linear ODEs
Modeling: Electric Circuits
The current I(t) in a certain LRC circuit obeys the differential equation 4I'' + 12I' + 25I = 10cos(5t/2) + 10sin(5t/2), with initial conditions I(0) = 0 and I'(0) = 0. Determine and identify its transient and steady state parts. Now assume the circuit has no resistance, so the differential equation becomes 4I'' + 25I = 10cos(5t/2) + 10sin(5t/2). Solve the initial value problem for the current I(t) if I(0) = 0 and I'(0) = 0.
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Watch the video solution with this free unlock.
EMAIL
PASSWORD