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1) RC Circuits: (15 pts) (a) Use Kirchhoff's voltage law (KVL) to obtain an ordinary differential...
electromagnetic 1) RC Circuits: (15 pts) (a) Use Kirchhoff's voltage law (KVL) to obtain an ordinary...
electromagnetic
1) RC Circuits: (15 pts) (a) Use Kirchhoff's voltage law (KVL) to obtain an ordinary differential equation (ODE) describing the charge vs. time function (1) for a capacitor in the discharging RC circuit shown below. Assume that at time t = 0 (right before the switch is closed) the voltage across the capacitor is V = V.. R R с V(t) С t=0 t>O Fig. 1. Fully charged RC circuit Fig. 2. Discharging RC Circuit (b) Solve the ODE...
Question 4: RC Circuit: a) Charging capacitor: A simple RC circuit is given in Figure 4a....
Question 4: RC Circuit: a) Charging capacitor: A simple RC circuit is given in Figure 4a. The capacitor is empty initially and switch was open for a long time. 4E, (V) EMF is used to charge the capacitor as switch is closed at t=0s. By using Kirchhoff's voltage law and Ohm's law that you learned so far, analyze this circuit and find the unknowns given below. 1)At t=0s. draw the equivalent circuit and find v. (Os), i. (Os), i (Os),...
Physics 1125 Monday Challenge Homework 7: RC circuits. Due on Monday March 9, 2020 at 8PM...
Physics 1125 Monday Challenge Homework 7: RC circuits. Due on Monday March 9, 2020 at 8PM Submit a PDF scan of your solution to the PHYS 1125 Canvas site. In this homework you will solve the same kind of first order differential equation you worked with last week. You can refer to that solution, you can even use Mathematica to do the work for you. Note that Mathematica can take care of the initial conditions as well, further simplifying what...
8. Capacitance in circuits, RC circuits When a voltage source Vo is applied to a capacitor...
8. Capacitance in circuits, RC circuits When a voltage source Vo is applied to a capacitor in a circuit which has a resistance R, a charge Q CV will build up across the capacitor. This does not happen instantaneously, but takes some time. The charge builds up exponentially with a characteristic time r = RC. Charging: V = v. 1 - e-t/RC) Discharging: Vc = V e-t/RC Page 2 of 3 When t = RC , the exponential is lle,...
5. [RC Circuits] Consider the circuit shown in Figure 5 attached. As shown, the switch is...
5. [RC Circuits] Consider the circuit shown in Figure 5 attached. As shown, the switch is in position "A" for t < 0, and the circuit has been at rest for a long time. At time t = 0, the switch opens and the capacitor starts to drain across the resistor. (a) When the switch is closed and there is only a direct current (DC) source, the capacitor acts like an open circuit. Find the constant voltage across the capacitor...
(1) Consider the RC circuit shown in Figure 1. For t<0 the switch is open, and...
(1) Consider the RC circuit shown in Figure 1. For t<0 the switch is open, and the charge stored on the capacitor is 0. At t-0 the switch is closed, and the voltage source begins charging the capacitor. Let R1-R2-220 Ω , C-0.47 μ F , Vs-5 V. (a) Write the differential equation as an expression for the capacitor voltage fort> 0 (i.e. write the differential equation) and calculate the time constant (b) Calculate the steady-state capacitor voltage R2 R1...
RC Circuits Case 1: Case 2: w V W v = R V = WM Consider...
RC Circuits Case 1: Case 2: w V W v = R V = WM Consider the two circuits. Initiall the switch is open, and then the switch is closed (completing the circuit). a) For Case 1: What is the current through the battery immediately after the switch is closed? Describe what happens to the current as a function of time, going to times much longer than any RC time constant. Why? b) For Case 1: What is the current...
Problem 1 Given the circuit shown below in Fig. 1.1: Write the ordinary differential equation (ODE)...
Problem 1 Given the circuit shown below in Fig. 1.1: Write the ordinary differential equation (ODE) for the capacitor voltage. Find the zero-state unit step responses of v(t) and i(t) if vs-u(t) V using each of the following three methods of solving the ODE: a. b. i. ii. Solve the ODE by integrating for the solution; Solve the ODE by assuming homogeneous and particular solutions; Solve the ODE by using the general form solution for a 1st order ODE. iii....
Power in RC Circuits- RC-9 A battery with &-15.0V is connected in series with a resistor...
Power in RC Circuits- RC-9 A battery with &-15.0V is connected in series with a resistor and capacitor in the circuit shown to the right. At r-0 the capacitor is uncharged and the switch is closed. a) Find the current in the circuit at t-1.00s. b) Find the rate at which the resistor is converting energy in the circuit into heat at t-1.00s. Hint: what are the units for the rate of transfer of energy? c) Find the rate at...
An RC circuit is connected across a DC voltage source through an open switch. The switch...
An RC circuit is connected across a DC voltage source through an open switch. The switch is closed at t = 0 s. Which of the following is a correct statement regarding the circuit? The capacitor charges to its maximum value in one time constant. The resistor and the capacitor share the applied voltage equally as a function of time. The current flows through the circuit even after the capacitor is fully charged. Once the capacitor is fully charged, there...
electromagnetic
1) RC Circuits: (15 pts) (a) Use Kirchhoff's voltage law (KVL) to obtain an ordinary differential equation (ODE) describing the charge vs. time function (1) for a capacitor in the discharging RC circuit shown below. Assume that at time t = 0 (right before the switch is closed) the voltage across the capacitor is V = V.. R R с V(t) С t=0 t>O Fig. 1. Fully charged RC circuit Fig. 2. Discharging RC Circuit (b) Solve the ODE...
Question 4: RC Circuit: a) Charging capacitor: A simple RC circuit is given in Figure 4a. The capacitor is empty initially and switch was open for a long time. 4E, (V) EMF is used to charge the capacitor as switch is closed at t=0s. By using Kirchhoff's voltage law and Ohm's law that you learned so far, analyze this circuit and find the unknowns given below. 1)At t=0s. draw the equivalent circuit and find v. (Os), i. (Os), i (Os),...
Physics 1125 Monday Challenge Homework 7: RC circuits. Due on Monday March 9, 2020 at 8PM Submit a PDF scan of your solution to the PHYS 1125 Canvas site. In this homework you will solve the same kind of first order differential equation you worked with last week. You can refer to that solution, you can even use Mathematica to do the work for you. Note that Mathematica can take care of the initial conditions as well, further simplifying what...
8. Capacitance in circuits, RC circuits When a voltage source Vo is applied to a capacitor in a circuit which has a resistance R, a charge Q CV will build up across the capacitor. This does not happen instantaneously, but takes some time. The charge builds up exponentially with a characteristic time r = RC. Charging: V = v. 1 - e-t/RC) Discharging: Vc = V e-t/RC Page 2 of 3 When t = RC , the exponential is lle,...
5. [RC Circuits] Consider the circuit shown in Figure 5 attached. As shown, the switch is in position "A" for t < 0, and the circuit has been at rest for a long time. At time t = 0, the switch opens and the capacitor starts to drain across the resistor. (a) When the switch is closed and there is only a direct current (DC) source, the capacitor acts like an open circuit. Find the constant voltage across the capacitor...
(1) Consider the RC circuit shown in Figure 1. For t<0 the switch is open, and the charge stored on the capacitor is 0. At t-0 the switch is closed, and the voltage source begins charging the capacitor. Let R1-R2-220 Ω , C-0.47 μ F , Vs-5 V. (a) Write the differential equation as an expression for the capacitor voltage fort> 0 (i.e. write the differential equation) and calculate the time constant (b) Calculate the steady-state capacitor voltage R2 R1...
RC Circuits Case 1: Case 2: w V W v = R V = WM Consider the two circuits. Initiall the switch is open, and then the switch is closed (completing the circuit). a) For Case 1: What is the current through the battery immediately after the switch is closed? Describe what happens to the current as a function of time, going to times much longer than any RC time constant. Why? b) For Case 1: What is the current...
Problem 1 Given the circuit shown below in Fig. 1.1: Write the ordinary differential equation (ODE) for the capacitor voltage. Find the zero-state unit step responses of v(t) and i(t) if vs-u(t) V using each of the following three methods of solving the ODE: a. b. i. ii. Solve the ODE by integrating for the solution; Solve the ODE by assuming homogeneous and particular solutions; Solve the ODE by using the general form solution for a 1st order ODE. iii....
Power in RC Circuits- RC-9 A battery with &-15.0V is connected in series with a resistor and capacitor in the circuit shown to the right. At r-0 the capacitor is uncharged and the switch is closed. a) Find the current in the circuit at t-1.00s. b) Find the rate at which the resistor is converting energy in the circuit into heat at t-1.00s. Hint: what are the units for the rate of transfer of energy? c) Find the rate at...
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