What is Rl circuit: Definition and 139 Discussions
A resistor–inductor circuit (RL circuit), or RL filter or RL network, is an electric circuit composed of resistors and inductors driven by a voltage or current source. A first-order RL circuit is composed of one resistor and one inductor and is the simplest type of RL circuit.
A first order RL circuit is one of the simplest analogue infinite impulse response electronic filters. It consists of a resistor and an inductor, either in series driven by a voltage source or in parallel driven by a current source.
For the period before ##t=0##, during which the switch was closed we have
$$-\epsilon_0+IR_1=-L\dot{I}\tag{1}$$
$$\dot{I}+\frac{R_1}{L}I=\frac{\epsilon_0}{L}\tag{2}$$
and the solution to this differential equation is
$$I(t)=\frac{\epsilon_0}{R_1}+e^{-\frac{R_1}{L}t}\tag{3}$$
Thus...
Just from looking at this circuit, we would expect the positive current to flow in a clockwise direction.
Let's define the normal vector pointing out of the screen. Then the positive circulation direction is counterclockwise.
I think that means that we have
I am not sure about the...
As far as I can tell we have
$$\mathcal{E}_L=\oint \vec{E}\cdot d\vec{l}=IR-\mathcal{E}=-L\dot{I}=-\dot{\Phi}\tag{1}$$
This differential equation can be written
$$\dot{I}+\frac{R}{L}I=\frac{\mathcal{E}}{L}\tag{2}$$
which is easily solved
$$I(t)=\frac{\mathcal{E}}{R}\left (...
I found the time constant using L/R and got 0.62s (3.6H/5.8ohms)
I found the initial current V/R and got 4.086A (23.7V/5.8ohms)
I(f) = 4.086A(1-e^(-0.5s/0.62s))
Then I plugged it into the equation and got 2.26A and it was wrong
##I_2 = \frac{V}{R_3 + R_2}e^{-t/\tau}##
##I_2 = \frac{50}{19.4(2)}e^{-t/\tau}## as t goes to 0, ##I_2 = \frac{50}{19.4(2)}## = 1.29 Amps which is not the answer.
What I have done:
(1) ##I(0)=\frac{V}{R}=\frac{1.5}{25}A=0.06 A.##
(2) By setting ##I(t*)=0.06(1-e^{-(35/0.4)t*})=35 mA## we get ##t*\approx 0.01 s##
What I have done seems correct to me, but the result for part (2) should be different.
I would be grateful if someone could point out to me...
I shorted the inductor and performed mesh analysis. The solutions to the linear system were done using a calculator. The book says that the value for i2(0-) should be 15 mA but I'm getting -2mA. What am I doing wrong? I'm completely confused. Maybe mesh isn't the most efficient way to find I2...
Hi guys , I've been trying to think this one out but I'm drawing a blank.
What I am able to understand that I'm required to calculate the backwards emf when the switch is opened. The current through the resistor R1 is 9mA. I was wondering if 9.2mA is even possible? Can the current exceed Imax...
In my idea the tension change after connecting the circuit to a battery is immediate, while the current takes some time before moving. That should be sufficient to prove my question but, so why in a RC circuit the opposite happens?
I already found ##I(t)## using Kirchhoff's laws, I got the equation ##V-RI-L\frac{dI}{dt}=0\Rightarrow L\frac{dI}{dt}=V-RI## then I solved the differential equation getting ##I(t)=\frac{V}{R}\left[1-e^{-\frac{R}{L}t}\right]##. My problem is founding the voltage as a function of time ##V(t)##, I...
Homework Statement
Homework Equations
[/B]
V = 1/L di/dt
I = Io x (1 - e^(-t/L/R)
Tau = L/RThe Attempt at a Solution
[/B]
Ii = 0mA ; If = 1mA
Vi = 1V ; Vf = 0V
Tau = 15uH / 1k Ohms = 10ns
If my above is correct, then voltage and current equations through inductor should be as follows...
Homework Statement
For the given circuits, identify state variables and derive a state-space model for each.
Assume the input is v(t) and the output is vL(t).
Homework EquationsThe Attempt at a Solution
[/B]
So my issue is that I solved this problem using two different methods. First...
Hi, I have just been refreshing my theory and was going over a parallel RL circuit, like this one.
The site I was reading had this for the total current
I tried some values as a test but it doesn't give me the correct answer, for total current. eg if I set
V=10V
R=2.5ohm
jXl=5ohm
Then...
Hi,
I'm struggling with source-free RL Circuit derivation.
In the books in the right side diagram they've reversed polarity of inductor to get equation:
V(r) = - V(L)
But why?
I checked google and everywhere they had put inductor with positive sign upwards.
Here is what I think--
In left...
Homework Statement
After a switch is left for a for many time constants, it is switched to b. find an expression for the total charge that passes through the resistor in one time constant
Homework Equations
dq/dt = I(t)
I(t) = (ε/R)(e^(-tR/l))
The Attempt at a Solution
so dq = I(t) dt
I know...
Hi guys,
I am working on a project that involves measuring the phase angle between two sinusoidal voltages. The circuit under examination is an RL type (the resistor was in series with the inductor), where the phase of voltage across the inductor is measured relative to the voltage input of the...
Homework Statement
In the circuit shown in (Figure 1) , the switch makes contact with position b just before breaking contact with position a. As already mentioned, this is known as a make-before-break switch and is designed so that the switch does not interrupt the current in an inductive...
For reference: Engineering Circuit Analysis, Hayt & Kemmerly, 4th ed, 1986, page 345.
Given a series RL circuit, the phasor current is I(s) = Vm/(R+sigma L), where S = sigma, w (omega) = 0. Thus we are dealing with only a exponential forcing function. Obviously I(s) goes to zero as sigma...
Homework Statement
From the textbook:
We define an energy function
\begin{equation}
V(\textbf{x},t) \leq 0
\end{equation}
for the system
\begin{equation}
\dot{\textbf{x}} = \textbf{f}(\textbf{x},\textbf{u},t).
\end{equation}
The function V may be the total energy of the system, or it may be...
Homework Statement
Here is the problem:
Homework Equations
Typical RL circuit equations.
The Attempt at a Solution
My main question with this problem is figuring out what to do with the third resistor, the one on the right. Initially, I thought of using RL circuit equations with the left...
as you can see In the image I provided I have derived the equation for i(t) and v(t).
On circuit A I use a passive sign convention(current flowing from positive to negative) on the inductor, hence the equation and their corresponding graph.
i(t) is decaying exponentially, v(t) is decaying...
as you can see In the image I provided I have derived the equation for i(t) and v(t).
On circuit A I use a passive sign convention(current flowing from positive to negative) on the inductor, hence the equation and their corresponding graph.
i(t) is decaying exponentially, v(t) is decaying...
1. The problem statement, all variables, and given/known data
I have a single loop RL circuit with no source. I am given the the inductance of 3mH, as well as that energy storage is as follows 1 J @ t=0 and 100mJ @ t=1ms. No current is given. I have to find R. I don't need the answer just some...
1. I thought that when switch was closed, voltage at the right side of switch was 0 and long time after the switch is open, the voltage at the right side of the switch becomes 0.
2. After the switch is open ecause of the inductor, voltage at the right side of the switch is εL = induced emf
So...
Homework Statement
Write the equations for the two mesh current i1 and i2. The circuit and the answer to mesh 1 are showing below
Homework EquationsThe Attempt at a Solution
My answer came out to be the same as the answer key except for the -25di1/dt term. It seems that this term gets...
I'm having some problems understanding why my computation deviates from solutions. I thank in advance to anyone who can give me some tips where I've gone wrong.
Homework Statement
Compute real power on resistors ## R_1 ## and ## R_2 ## and reactive power on inductor ## L ##. Circuit is powered...
Homework Statement
I am practicing questions from the book in preparation for an exam, and I am having trouble with this one
Homework EquationsThe Attempt at a Solution
According to my professor, the answers are: R1=12ohm, R2=9ohm, L=34.28 H
So far this is what I have done:
Voc = 6V
τ = 20/7...
Homework Statement
Initially switch is at 0.
At t = 0 seconds switch is put at 1.
After 1 time constant switch is put at 2.
Find equation for current for t > 2[/B]
Homework Equations
current through inductor tries to remain constant.
i(t) through inductor in series RL circuit is i(t) = [...
Hi, I can't figure out what is the physical reason behind the fact that, in DC RL circuit, for example, the series one, the current rises from zero (supposing state zero response), to its maximum value given by ohm's law. I've understood it mathematically but I can't physically explain why...
This isn't a homework question! I posted the question for context purpose.
So I understand that at t>0 the switch moves to b. Hence the first circuit diagram (pictured) I understand.
However for the 2nd circuit diagram (picture 2) when asked to transform to s domain. Why does this answer...
Sorry
this is the first time i come to this forum.
Why the -Ldi/dt in the left side is minus but not plus sign
i got confused
Does everyone can help me in this problem
thank you
-------------------------------------------------------------
i know V-Ri-Ldi/dt=0 is true in the right hand...
Homework Statement
http://imgur.com/ZKiCbbA http://imgur.com/a/ccGTV
Could someone explain me what happened in the step that is circled in red please? I would appreciate it.
did they multiply i0x(iL)?
Homework Equations
they got iL by using iL=iL(initial)*e^-t/Tau . How did they get Vo? what...
Homework Statement
Homework Equations
V=IRThe Attempt at a Solution
This problem is really confusing me. For VL(0-) and IL(0-), the voltage and current when t<0, wouldn't both those values just be 0? the 0- means before the switch is closed right? So before it is closed the right branch...
Homework Statement
Homework EquationsThe Attempt at a Solution
I would show my working, but honestly, I'd really just like a hint as to how to begin, because I've tried multiple different things and just gotten tangled up in multiple equations that are way more complicated looking than the...
Homework Statement
Homework EquationsThe Attempt at a Solution
When the t < 0, the switch is open, the inductor acts like a short therefore the circuit looks like
The current is then 20V / 4 ohms = 5 A
Since the inductor has been in series with the battery for a long time, it is safe to...
Homework Statement
For a simple series LR circuit, find the energy delivered to the circuit by the battery.
Homework Equations
I = (V/R)*(1-e-Rt/L)
P=IV
E=∫Pdt
The Attempt at a Solution
Isn't ∫ Pdt = ∫ IVdt = ∫ (V2/R)*(1-e-Rt/L)dt = (V2/R)(t + (L/R)e-Rt/L) ?
The book provides the answer, via...
Hi there,
I'm struggling to wrap my head around a 'should-be-simple' problem involving an RL circuit. Referring to the image I've pasted below, what happens if we were to remove switch 1, and instead created a scenario where switch 2 simply opens? Where would the current go in the inductor?
I...
Homework Statement
This isn't so much of a problem itself but I found it interesting that on the All About Circuits website, two of the questions give a phase angle for impedance as opposite the angle of current. I understand the current is 90 degrees out of phase with voltage in both RL and RC...
Hello! It's a pretty long time time since I did my last circuit analisys, so I feel a bit rusty.
I have to calculate the evolution of current in the inductor:
L is generic and u(t) is the Heaviside step function. Do note that at t = 0 the inductor behaves like a short circuit (I don't know...
Hi,
I have a qualitative question about RL circuits. I'm trying to summarize how R and L each affect the transient response time L/R from the perspective of energy transfers. I'm pretty confident in my description of the influence of L. I'm not very confident in my description of R in the case...
Homework Statement
There is a DC circuit with a resistor and inductor in parallel. Graph the current through the resistor vs time and the inductor vs. time.
Homework Equations
i=i(0)e^(-Rt/L)+V/R(1-e^(RT/L)
The Attempt at a Solution
My first thought was that initially current through the...
Homework Statement
The attachment shows the circuit in question. Pardon the crude drawing. The top circuit is the circuit drawn in the text. The middle circuit is how the circuit is supposed to behave for t < 0 (switched closed). The bottom circuit is how the circuit is supposed to behave for t...
Suppose there is a circuit consisting of a battery, a resistor, and an inductor, and that there is initially no current. As current is increasing, the inductor creates an induced current in the opposite direction. I am confused as to which end of the inductor is at a higher voltage. Since the...
Homework Statement
For the circuit in the attached file, find io (current) for t>0
Homework Equations
The Attempt at a Solution
I have included an attachment which shows the solution. However, I will copy the solution here as well for reference:
When t<0, the switch is closed, the inductor...
Homework Statement
(see figure)[/B]
The switch is initially open for a long time.
At t=0 it is closed, and after 1ms it is reopened.
Find the voltage across Resistor 2 at (i)0<t<1ms and (ii) t>1ms.
Homework Equations
V0=120V
R1=500 Ω
R2=125 Ω
Inductance of the inductor = 0.2 H
The Attempt at...
Homework Statement
Determine the inductor current i(t) for both t<0 and t>0 for the circuit shown in the attached document"Circuit 1.
Homework EquationsThe Attempt at a Solution
Before t=0, i=(25)/(3+2) = 5A
After t=0, i(t)=i(0)e^(-t/tow)
tow=L/R=4/(6/5)
However, the...
Homework Statement
The circuit above has a 29 resistor and a 11.1 mH inductor. Calculate the theoretical phase difference between the current CPA and voltage VPB if the circuit is driven by a sinusoidal voltage source with a peak amplitude of 3.5 V at the following frequencies:
20 Hz
420 Hz...
Homework Statement
A simple RL circuit in series connected to a source with V(t) = 30Cos(3t+75°)V and is delivering 14.12 W of power. I'm also given the power factor which is pf=0.857 and is lagging.
Find the values of R and L
Homework Equations
P=Vm*Im/2 * pf for power
theta =...
Homework Statement
Homework Equations
iL = (iL(0) + Vs/R)e(-t/τ + Vs/R
The Attempt at a Solution
When the switch is closed before t=0, v(t) = 100V as the first 100Ohm resistor is shorted and L acts as a short wire in DC steady state.
When the switch opens, v(t) = 50V by voltage divider...