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Questions and Answers
What is the solution to the non-homogeneous differential equation representing the current in the RL circuit?
What is the solution to the non-homogeneous differential equation representing the current in the RL circuit?
- $i = Ke^{-t/\tau} - V$
- $i = Ke^{-t/\tau} + V$
- $i = Ke^{-t/\tau} - \frac{V}{R}$
- $i = Ke^{-t/\tau} + \frac{V}{R}$ (correct)
What type of differential equation is the equation describing the transient response of the RL circuit?
What type of differential equation is the equation describing the transient response of the RL circuit?
- Non-linear differential equation of second order
- Linear differential equation of first order (correct)
- Homogeneous differential equation of first order
- Non-homogeneous differential equation of first order
How is the value of the arbitrary constant 'K' determined in the current equation for the transient response of the RL circuit?
How is the value of the arbitrary constant 'K' determined in the current equation for the transient response of the RL circuit?
- By taking the derivative of the current equation
- By integrating the voltage equation
- By using the initial conditions (correct)
- By applying Kirchhoff's current law
What is the applied constant voltage 'V' in the equation describing the transient response of the RL circuit?
What is the applied constant voltage 'V' in the equation describing the transient response of the RL circuit?
What happens to the inductor in the RL circuit when the switch S is closed?
What happens to the inductor in the RL circuit when the switch S is closed?
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Study Notes
RL Circuit Transient Response
- The solution to the non-homogeneous differential equation representing the current in the RL circuit involves finding the general solution and the particular solution, then combining them to obtain the complete solution.
Differential Equation Type
- The equation describing the transient response of the RL circuit is a first-order linear differential equation.
Determining the Arbitrary Constant 'K'
- The value of the arbitrary constant 'K' is determined by applying the initial condition, i.e., the current at time t = 0, to the general solution.
Applied Constant Voltage 'V'
- The applied constant voltage 'V' in the equation describing the transient response of the RL circuit is the voltage source connected to the RL circuit.
Inductor Behavior when Switch S is Closed
- When the switch S is closed, the inductor in the RL circuit starts to store energy, causing the current to increase gradually, and the magnetic field around the inductor builds up.
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