Solving Ri(t)+Ld$\frac{di(t)}{dt}=V_{m}sin(wt+\theta)

Thread starter aztect
Start date Sep 10, 2006

In summary, the equation "Solving Ri(t)+Ld$\frac{di(t)}{dt}=V_{m}sin(wt+\theta)" represents the relationship between voltage, current, and time in a circuit with a resistor, inductor, and sinusoidal voltage source. It can be solved using differential equations and complex numbers, and the parameters in the equation represent the resistance, inductance, maximum voltage, frequency, and phase angle. However, it is not applicable to all types of circuits. This equation has various real-world applications in electrical circuit analysis, power systems, electronic devices, and electromagnetic studies.

Sep 10, 2006

aztect

Can anyone help me with this?
[tex]Ri(t) + L\frac{di(t)} {dt}=V_{m}sin(wt+\theta)[/tex]

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Sep 10, 2006

arildno

Science Advisor

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Hint:
What is the integrating factor here?

Sep 10, 2006

aztect

[tex]\exp\int\frac{R}{L}dt[/tex]?

Sep 10, 2006

arildno

Science Advisor

Homework Helper

Gold Member

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Which can be written more simply as..:?(assuming R, L constants, that is)

Sep 11, 2006

aztect

[tex]\exp\int{x}dt[/tex]

1. What does the equation "Solving Ri(t)+Ld$\frac{di(t)}{dt}=V_{m}sin(wt+\theta)" represent?

This equation represents the relationship between voltage, current, and time in a circuit with a resistor (R), inductor (L), and voltage source (Vm) with a sinusoidal wave of frequency w and phase angle θ.

2. How is this equation solved?

This equation can be solved using differential equations and complex numbers. The solution involves finding the particular solution for the forced response and the complimentary solution for the natural response of the circuit.

3. What is the significance of the parameters in this equation?

The parameter R represents the resistance of the circuit, L represents the inductance, Vm represents the maximum voltage of the source, w represents the frequency of the sinusoidal wave, and θ represents the phase angle.

4. Can this equation be used to solve any type of circuit?

No, this equation is specifically used for circuits with a resistor, inductor, and sinusoidal voltage source. It is not applicable to circuits with other components or different types of voltage sources.

5. What are some real-world applications of this equation?

This equation is commonly used in the analysis and design of electrical circuits, such as in power systems, electronic devices, and communication systems. It can also be used in the study of electromagnetic phenomena and the behavior of electrical signals.