Please do the problem if you can do ALL parts. t-0 a SW1 SW2 0.5 Ω 2 1Ω V. R3 20 A T v(t) 0.5 F 0.5 H 0 Find the initial current i(0) through the inductor and the initial voltage v(0) across the capacitor at t 0. b. Write a node equation at node a fort2 0. c. Represent v(t) as a function of i(t) on the series connection of R2 and L. Find dv(t)/dt. Derive a second-order differential...
do not use s domain method ,use only differential equation 3. In the circuit shown, switch 1 has been closed for a long time before it is opened at t 0, and switch 2 has been opened for a long time before it is closed at t = 0. SW2 sw, 0.5Ω R2 1(2 A, 20 A i(t) 0.5 H a. Find the initial voltage v(O)- Vo across the capacitor and initial current through the inductor (0) lo at t...
5) (15) P4.18. Consider the circuit shown in Figure P4.18. Prior to t0, 100 V, and v20. a. Immediately after the switch is closed, what is the value of the current [i.e., what is the value of i(0+)]? b. Write the KVL equation for the circuit in terms of the current and initial voltages. Take the derivative to obtain a differential equation. c. What is the value of the time constant in this circuit? d. Find an expression for the...
For the circuit shown, find the following: a) v(0+), the voltage across the capacitor right after the switch closes. b) v), the voltage across the capacitor after the switch has been closed for a long time. c) v(T), the voltage across the capacitor after one time constant. 2. 3 S2 I(t) 12 V+ 6 Ω 0.5 F u(t) 3. For the circuit above, write the differential equation for t > 0.
dx dt 1. For the circuit below determine: a) The initial conditions: iz(0+), dix(0*), v(0+), dv(0+) b) The circuit differential equation and solve for iz(t), t 2 0 (No credit for Transform techniques) ix VI 102 422 + lo 5+10u(t) 10 H 1/4 F V
4. In the circuit shown, R - 500 ohm, L -0.64 H, C - 1u F, 1- -1 A, Vcap (o) -40 v, indur (o ) - 0.5 A. Find a. IR (o) b. Derive a differential equation for current Derive an expression for the v(t) c. C 3 4. In the circuit shown, R - 500 ohm, L -0.64 H, C - 1u F, 1- -1 A, Vcap (o) -40 v, indur (o ) - 0.5 A. Find a....
8.43 The initial conditions for the circuit shown in Figure P8.43 are i(0) = 1 = 1 A, v(0) = V. = 2 V. FIGURE P8.43 w 40 a. Write a node equation at node a by summing the currents leaving node a fort 20. Find di(0)/dt. b. Write a node equation at node b by summing the currents leaving node b for t 2 0. c. Find the differential equation in i(t) and find the roots of the characteristic...
1.(20 pts) The switch in the circuit shown below has been closed for a long time before it is opened at -0. (a) Is this RL or RC switching circuit. (b) Is this Natural or Step Response for t0? (c) Find veo'). (d) What is the time constant t of the circuit for t0? (e) Find Vco). (1) Write the expression for vct) fort >0. (g) Write the expression for ict) fort >0. (h) Write the expression for i(t) fort...
3. A circuit contains a switch, a switch is closed at t0 = 10 V battery, a Imax-20 A fuse, and a L = 5.0 H inductor. The ImAx (a) Write a loop equation for the circuit to find a relation between dI/dt, L and ε (b) Integrate the result of part a to find the I at a function of time t with parameters to fully specify I(t) you must consider the initial value of the current. and L....
5. Determine v(t) for t < 0 and t > 0 in the circuit shown 0.5 H 0 3? 8? 4i0 24 V (+ 20v