Transient RC Circuit (got answer in s but not in t-domain)

In summary, the conversation discusses solving a circuit problem involving a capacitor and using Laplace method to find the answer. However, the book answer points out that the polarity of the capacitor's initial voltage is not given, which is crucial in solving the problem. The solution is eventually found by assuming the polarity of the lower plate to be positive.
  • #1
jaus tail
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Homework Statement


upload_2018-1-24_11-45-7.png


Homework Equations


Vc = ( Initial Voltage - Final Voltage ) e(-RC/t) + Final Voltage

3. The Attempt at a Solution
I got the answer through Laplace but am not getting through time domain analysis.
Given q across C is 2.5mC
C = 50micro F
q = CV
So V = 50V
Initial voltage = 50V
Final voltage = 100V since C will be open circuit on steady state.
Req = 10 ohm
Ceq = 50 micro F
RC = .0005
1/RC = 2000
So applying the underlined formula I get Vc = ( 50 - 100) e(-2000t) + 100
Ic = C dV/dt = 50 micro times (-50 * -2000) e(-2000t)
Ic = 5e(-2000t)

Book answer is A.
 

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  • #2
The polarity of the capacitor initial voltage is not indicated so you can't solve the problem.
 
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Likes jaus tail
  • #3
Oh yeah. I tried with polarity of lower plate positive and got answer in time domain. Thanks.
 

1. What is a transient RC circuit?

A transient RC circuit is an electrical circuit that contains a resistor (R) and a capacitor (C) in series. It is called a transient circuit because it deals with the temporary changes in voltage and current that occur when a circuit is turned on or off.

2. How does a transient RC circuit work?

In a transient RC circuit, when the circuit is turned on, the capacitor initially acts as an open circuit, allowing the full voltage to be applied across it. As time passes, the capacitor charges up and the voltage across it decreases. This process is known as transient response and it creates a voltage drop across the resistor, resulting in a decrease in current.

3. What is the time constant in a transient RC circuit?

The time constant (τ) in a transient RC circuit is a measure of how quickly the capacitor charges up. It is calculated by multiplying the resistance (R) and the capacitance (C) in the circuit. A larger time constant means the capacitor will take longer to charge, resulting in a longer transient response.

4. How is a transient RC circuit analyzed?

A transient RC circuit can be analyzed using Kirchhoff's laws and the equations for voltage and current in a series RC circuit. The equations can be solved using techniques such as substitution or integration to find the voltage and current at any given time in the circuit.

5. What are some practical applications of transient RC circuits?

Transient RC circuits have many practical applications, such as in electronic devices that require a smooth and gradual change in voltage or current. They are also used in filters, sensors, and timing circuits. Additionally, transient RC circuits are an important concept in understanding the behavior of more complex circuits and systems.

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