In this situation, y (t) = x (t), where x (t) is the voltage input and y (t) is the voltage output across the capacitor. Now, my intuitive understanding tells me that the zero-input response is zero because no current has been provided yet and the capacitor is uncharged. But what about the zero-state response?
To find the constant A for the zero input response of a series RC circuit, you can use the initial condition at time t = 0. The initial voltage V0 across the capacitor is given. The constant A is simply the initial voltage V0. Using k = –1/RC, you can find the solution to the differential equation for the zero input.
The zero input part of the response is the response due to initial conditions alone (with the input set to zero). The zero state part of the response is the response due to the system input alone (with initial conditions set to zero). The complete response is simply the sum of the zero input and zero state solutions.
That means that whatever variation of voltage exists, the capacitor will follow exactly, while the current through it will be infinite in value. Make that impossible, since I=V/R, unless you have special cherokee blood. In short, there is no zero-input since there is a voltage source involved, and zero-state means whatever the source has.
Zero input voltage means having no input for all time. The output response is determined by the initial condition V0 (initial capacitor voltage) at time t = 0. The first-order differential equation simplifies to Here, vZI(t) is the capacitor voltage.
From my understanding, the zero-input and zero-state responses of an RC circuit can be found by solving for the homogenous and particular solution of the ordinary differential equation found using Kirchhoff's current law. But I am confused as to what happens if there is no resistor in the circuit.
Chapter 9 Transient Response
Zero-input response: the circuit has no applied source after a certain time. It is determined by natural response and the initial condition. Zero-state response: the circuit has no initial stored energy. ( t : time constant) eq t = í (If t<0, then the circuit is unstable.)
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RC Circuit Analysis: Series & Parallel (Explained in ...
The natural response is one in which source of supply is turned off but the circuit does including the initial conditions (initial voltage on capacitors and current in inductors). The natural response is also called the zero input response because the source of supply is turned off. Therefore, total response = forced response + natural response
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Zero state response
The Zero State Response () represents the system output () when () =. When there is no influence from internal voltages or currents due to previously charged components = ().Zero state response varies with the system input and under zero-state conditions we could say that two independent inputs results in two independent outputs:
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Zero-input response basics
Total response = zero-input response + zero-state response In this lecture, we will focus on a linear system''s zero-input response, y 0 (t), which is the solution of the system equation when input x(t) = 0. Zero-input response basics L2.2 p152 ⇒ ⇒ ⇒ PYKC 24-Jan-11 E2.5 Signals & Linear Systems Lecture 3 Slide 3
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Capacitors Initial and Final Response to a "Step Function"
Capacitors Initial and Final Response to a "Step Function" • Inductors and Capacitors react differently to a Voltage step • Just after the step Capacitors act as a short if uncharged dt dV IC(t )=C • If charged Capacitor acts as an voltage source • As time goes to infinity change in …
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RC Circuit Analysis: Series & Parallel (Explained in ...
Zero-input response: the circuit has no applied source after a certain time. It is determined by natural response and the initial condition. Zero-state response: the circuit has no initial stored …
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Capacitors Initial and Final Response to a "Step Function"
Capacitors Initial and Final Response to a "Step Function" • Inductors and Capacitors react differently to a Voltage step • Just after the step Capacitors act as a short if uncharged dt dV …
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The Complete Response of RL and RC Circuits
Natural response: the general solution of the (homogeneous) differential equation representing the first-order circuit, when the input is zero. when there is non-zero input. The constant K in …
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Find the Zero-Input and Zero-State Responses of a Series RC
Zero-state response means zero initial conditions, and it requires finding the capacitor voltage when there''s an input source, v T (t). You need to find the homogeneous and particular solutions to get the zero-state response. To find zero initial conditions, you look at the circuit when there''s no voltage across the capacitor at time
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Natural Response of RC and RL Circuits
Natural response is also called zero‐input response (ZIR). Natural response comes from initial conditions in the circuit, like initial currents in inductors or initial voltages or charge on …
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Natural Response of RC and RL Circuits
Natural response is also called zero-input response (ZIR). Natural response comes from initial conditions in the circuit, like initial currents in inductors or initial voltages or …
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systemresponse
The voltage source has zero internal resistance (not infinite, that''s a current source). A capacitor across it will have whatever potential exists at the source''s pins. That means that whatever variation of voltage exists, the capacitor will follow exactly, while the current through it will be infinite in value. Make that impossible ...
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SECTION 4: SECOND-ORDER TRANSIENT RESPONSE
Second-order, RLC step response. K. Webb ENGR 202 Transient Response of Second-Order Circuits. 4. K. Webb ENGR 202 5 Second-Order Transient Response In ENGR 201 we looked at the transient response of first-order RC and RL circuits Applied KVL Governing differential equation Solved the ODE Expression for the step response For second-order circuits, process …
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Signals and Systems
Think of a discharged capacitor being charged by a voltage source through a resistor. An amplifier is not a dynamic system, so if there is no input there is no output. In this lecture, we will focus on a linear system''s zero-input response, 0( ), which is the solution of the system''s equation when input = 0. (∙) = is the th derivative.
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Solved + x(1) C R M + Figure 1: RLC circuit 3 Determine | Chegg
Question: + x(1) C R M + Figure 1: RLC circuit 3 Determine the zero-input response given an initial capacitor voltage of one volt and an initial inductor current of zero amps. That is, find yo(t) given uc(0) = 1V and iz(0) = 0A. [Hint: The coefficient (s) in yo(t) are independent of L and C.] 4 Plot yo(t) for t > 0. Does the zero-input response ...
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8.4: Transient Response of RC Circuits
This is known as the transient response. Consider the circuit shown in Figure 8.4.1 . Note the use of a voltage source rather than a fixed current source, as examined earlier. Figure 8.4.1 : A simple RC circuit. The key to the analysis is to remember that capacitor voltage cannot change instantaneously. Assuming the capacitor is uncharged, the instant power is applied, the …
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Signals and Systems
Think of a discharged capacitor being charged by a voltage source through a resistor. An amplifier is not a dynamic system, so if there is no input there is no output. In this lecture, we will focus …
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Transient response of RC and RL circuits
In many applications, these circuits respond to a sudden change in an input: for example, a switch opening or closing, or a digital input switching from low to high. Just after the change, the capacitor or inductor takes some time to charge or discharge, and eventually settles on its new steady state. We call the response of a circuit immediately after a sudden change the transient …
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Natural Response of RC and RL Circuits
Natural response is also called zero‐input response (ZIR). Natural response comes from initial conditions in the circuit, like initial currents in inductors or initial voltages or charge on capacitors. The natural response of an RL or RC circuit with no sources is described by a homogeneous linear differential equation. This chapter describes ...
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RC Circuit Analysis: Series & Parallel (Explained in
The natural response is one in which source of supply is turned off but the circuit does including the initial conditions (initial voltage on capacitors and current in inductors). The natural response is also called the zero input …
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Zero Input & Zero State Response
Key Concept: Zero Input, Zero State and Complete Response. The transient response of a system can be found by splitting a problem into two parts. The zero input part of the response is the response due to initial conditions alone (with …
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The Complete Response of RL and RC Circuits
Natural response: the general solution of the (homogeneous) differential equation representing the first-order circuit, when the input is zero. when there is non-zero input. The constant K in the natural response depends on the initial condition. For example, the capacitor voltage at time t0. In this chapter, we will consider three cases.
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Capacitor Transient Response | RC and L/R Time Constants
The capacitor voltage''s approach to 15 volts and the current''s approach to zero over time is what a mathematician would describe as asymptotic: that is, they both approach their final values, getting closer and closer over time, but never exactly reach their destinations. For all practical purposes, though, we can say that the capacitor voltage will eventually reach 15 volts and that …
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Signals and Systems
Total response = zero-input response + zero-state response ... discharged capacitor being charged by a voltage source through a resistor. • An amplifier is not a dynamic system, so if there is no input there is no output. Total response of dynamic systems cont. • In this lecture, we will focus on a linear system''szero-input response, 0(𝑡), which is the solution of the system ...
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Natural Response of RC and RL Circuits
Natural response is also called zero-input response (ZIR). Natural response comes from initial conditions in the circuit, like initial currents in inductors or initial voltages or charge on capacitors. The natural response of an RL or RC circuit with no sources is described by a homogeneous linear differential equation. This chapter describes the RC and RL natural …
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systemresponse
The voltage source has zero internal resistance (not infinite, that''s a current source). A capacitor across it will have whatever potential exists at the source''s pins. That means that whatever variation of voltage exists, the …
Learn More
Natural Response of RC and RL Circuits
Natural response is also called zero-input response (ZIR). Natural response comes from initial conditions in the circuit, like initial currents in inductors or initial voltages or charge on capacitors. The natural response of an RL or RC circuit with no sources is described by a homogeneous linear differential equation. This chapter ...
Learn More
Zero Input & Zero State Response
Key Concept: Zero Input, Zero State and Complete Response. The transient response of a system can be found by splitting a problem into two parts. The zero input part of the response is the response due to initial conditions alone (with the input set to zero).
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