Differential Equations and Circuits

In summary, the book justified grouping the I term with the dI, but I don't understand why the L, V, and R terms are placed as they are? Can you get the same result if they were not arranged in this way?
  • #1
nikki__10234
3
0
So, I'm learning how to solve LR, RC, LC etc. types of circuits using differential equations. I understand how to do the math with differential equations, but I am confused as to why the variables are split in the way they are.

For example, for an LR circuit you have the equation
L(dI/dt)+RI=V

and then the book integrates both sides:
∫(dI/(V-IR))=∫(dt/L)
and so on...

It is justified to group the I term with the dI, but I don't understand why the L, V, and R terms are placed as they are? Could you get the same result if they were not arranged in this way since the integral is not being taken in terms of V, R or L?
 
Physics news on Phys.org
  • #2
welcome to pf!

hi nikki! welcome to pf! :smile:
nikki__10234 said:
L(dI/dt)+RI=V

and then the book integrates both sides:
∫(dI/(V-IR))=∫(dt/L)
and so on...

It is justified to group the I term with the dI, but I don't understand why the L, V, and R terms are placed as they are? Could you get the same result if they were not arranged in this way since the integral is not being taken in terms of V, R or L?

the V has to stay with the IR …

can you see any way of getting the IR over onto the LHS (with the dI), without the V coming with it?​

but the L could go either side
 
  • #3
nikki__10234 said:
So, I'm learning how to solve LR, RC, LC etc. types of circuits using differential equations. I understand how to do the math with differential equations, but I am confused as to why the variables are split in the way they are.

For example, for an LR circuit you have the equation
L(dI/dt)+RI=V

and then the book integrates both sides:
∫(dI/(V-IR))=∫(dt/L)
and so on...

It is justified to group the I term with the dI, but I don't understand why the L, V, and R terms are placed as they are? Could you get the same result if they were not arranged in this way since the integral is not being taken in terms of V, R or L?
The only requirement is that any variables which actually vary in the range of integration stay inside an integral, but it will help if it varies as a function of the variable of integration with which it is placed.
E.g. if L = L(t) then it would best be placed in the integral .dt as above, whereas if R is a constant then you could just as easily write
∫(dI/(V/R-I))=R∫(dt/L)
OTOH, if V = V(t) it's going to get tricky ;-).
 

1. What are differential equations and how are they used in circuits?

Differential equations are mathematical equations that involve rates of change and are used to describe the behavior of dynamic systems. In circuits, differential equations are used to model the relationship between the input voltage, current, and the output voltage, current, and how they change over time.

2. What is the difference between a linear and non-linear differential equation in circuit analysis?

A linear differential equation is one in which the dependent variable and its derivatives appear only in a linear form. This means that the output is directly proportional to the input. Non-linear differential equations, on the other hand, involve terms with powers and products of the dependent variable and its derivatives, making the relationship between output and input more complex.

3. How do you solve differential equations in circuit analysis?

There are several methods for solving differential equations in circuit analysis, including using analytical techniques such as separation of variables or Laplace transforms, or using numerical methods such as Euler's method or Runge-Kutta methods. The method used will depend on the complexity of the circuit and the desired level of accuracy.

4. Can differential equations be used to analyze both AC and DC circuits?

Yes, differential equations can be used to analyze both AC (alternating current) and DC (direct current) circuits. However, the equations and methods used may differ depending on the type of circuit and the input signal. For example, AC circuits may involve the use of complex numbers and phasors, while DC circuits typically use real numbers.

5. What are some real-world applications of differential equations in circuit analysis?

Differential equations are used in circuit analysis to design and analyze a wide range of electrical systems, from simple circuits used in electronics to complex power systems used in large-scale industries. They are also used in the development of electronic devices such as computers, smartphones, and medical equipment. Additionally, differential equations are essential in understanding and predicting the behavior of electric motors, generators, and transmission lines in power systems.

Similar threads

I How can engineers get away with splitting differentials in dynamics?
    • Classical Physics
Replies
3
Views
2K
I Outright understanding L/R inductor time constant
    • Classical Physics
Replies
2
Views
786
I Pushing a rod in a magnetic field
    • Classical Physics
Replies
15
Views
529
Solving a Non-Homogeneous Linear Differential Equation
    • Calculus and Beyond Homework Help
Replies
12
Views
1K
I Equation of motion: choice of generalized coordinates
    • Classical Physics
Replies
14
Views
1K
A F.E.M and Hamilton's Principle (converting differential equations into integral equations)
    • Classical Physics
Replies
1
Views
711
I Sign of the terms in a circuit
    • Classical Physics
Replies
4
Views
868
I The far reaching ramifications of the work-energy theorem
    • Classical Physics
Replies
31
Views
2K
Introduce a battery to an LR circuit
    • Introductory Physics Homework Help
Replies
16
Views
210
I Alternative Approach to Solving Foucault's Pendulum Behavior
    • Classical Physics
Replies
8
Views
1K

Hot Threads

Recent Insights

Back
Top