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Questions and Answers
What type of response occurs in an RL circuit when an inductor is connected to a DC source and energy is released into a resistive network?
What type of response occurs in an RL circuit when an inductor is connected to a DC source and energy is released into a resistive network?
- Steady-state response
- Natural response (correct)
- Step response
- Transient response
What is the time constant for an RL circuit?
What is the time constant for an RL circuit?
- $\tau = R \cdot L$
- $\tau = \frac{R}{L}$
- $\tau = \frac{L + R}{L}$
- $\tau = \frac{L}{R}$ (correct)
What is the power dissipated in a resistor in an RL circuit?
What is the power dissipated in a resistor in an RL circuit?
- $I_0^2 (1 - e^{-\frac{2R}{L}t})$
- $I_0^2 (1 + e^{-\frac{2R}{L}t})$
- $\frac{1}{2} LI_0^2 (1 - e^{-\frac{2R}{L}t})$
- $I_0^2 e^{-\frac{2R}{L}t}$ (correct)
What happens after the transient response in an RL circuit?
What happens after the transient response in an RL circuit?
How does the natural response of an RL circuit decay over time?
How does the natural response of an RL circuit decay over time?
What is the general method for finding step and natural responses in RL circuits?
What is the general method for finding step and natural responses in RL circuits?
In an RL circuit, what occurs before the steady-state response?
In an RL circuit, what occurs before the steady-state response?
What does the time constant represent in an RL circuit?
What does the time constant represent in an RL circuit?
What condition is assumed just before the switch opens in an RL circuit according to the text?
What condition is assumed just before the switch opens in an RL circuit according to the text?
How does the inductor behave just before it begins releasing energy in an RL circuit?
How does the inductor behave just before it begins releasing energy in an RL circuit?
When does the inductor begin releasing energy in an RL circuit?
When does the inductor begin releasing energy in an RL circuit?
What happens to the entire source current just before the switch opens in an RL circuit?
What happens to the entire source current just before the switch opens in an RL circuit?
When is the voltage and current at the terminals of the resistor R found in an RL circuit?
When is the voltage and current at the terminals of the resistor R found in an RL circuit?
What do we assume about the current source just before the switch opens in an RL circuit?
What do we assume about the current source just before the switch opens in an RL circuit?
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Study Notes
- Lecture objective: analyze natural response of first-order systems and step response, demonstrate general solution for step and natural responses in RL circuits.
- RL circuits consist of a resistor and an inductor, described by a first-order differential equation.
- Natural response occurs when an inductor/capacitor is connected to a DC source and energy is released into a resistive network.
- Step response occurs when a DC source is connected to an inductor/capacitor to store energy.
- General method for finding step/natural response for any RL or RC circuit to be discussed later.
- Differential equation for natural response in RL circuit: (I(t) = I(0) e^{-\frac{R}{L}t}).
- Time constant ((\tau)) for an RL circuit: (\tau = \frac{L}{R}), significance in relation to current decay.
- Transient response occurs before 5 time constants, steady-state response after.
- Power dissipated in resistor: (I_0^2 e^{-\frac{2R}{L}t}), energy delivered to resistor: (0.5 LI_0^2(1 - e^{-\frac{2R}{L}t})).
- Steps for finding natural response in RL circuit: find initial current, calculate time constant, use (I(t) = I(0) e^{-\frac{t}{\tau}}) to find (I(t)) and other circuit values.
- Example problems demonstrated for finding current and voltage in RL circuits with detailed calculations and circuit analysis.
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