RC-RL Circuit: Solving for Capacitance Value

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In summary: If you set up and solve the 1st order D.E. this should be confirmed.In summary, the homework statement is trying to find the current and voltage of a circuit with a capacitor, and the student is trying to figure out why the value of the current is different depending on whether or not there is initial charge on the capacitor.
  • #1
paulmdrdo
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Homework Statement


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2. Homework Equations
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3. The Attempt at a Solution
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In got stuck. I'm not sure as to what Time constant should I use to solve for the capacitance value. In the original expression for the current, both terms are exponential function. I do not know whether to use the time constant associated with the first term or the second term.
 

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  • #2
The voltage of the source is given by ##V_s(t)=36e^{-t}u(t)## ?? What function is ##u(t)##?
 
  • #3
Delta2 said:
The voltage of the source is given by ##V_s(t)=36e^{-t}u(t)## ?? What function is ##u(t)##?
That's a unit step function.
 
  • #4
Well ok, I am not 100% sure but I believe the second exponential contains info about the capacitance. More specifically I think that ##\frac{1}{(R_1+R_2)C}=0.6##
 
  • #5
Delta2 said:
Well ok, I am not 100% sure but I believe the second exponential contains info about the capacitance. More specifically I think that ##\frac{1}{(R_1+R_2)C}=0.6##
Thank you. That's what I thought too. But It would be nice if someone would explain as to why that is the case.
 
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  • #6
paulmdrdo said:
Thank you. That's what I thought too. But It would be nice if someone would explain as to why that is the case.
.

By setting up and solving the differential equation for this circuit and using that ##V_s(t)=36e^{-t}## I found that the current is $$I(t)=ae^{-t}+be^{-\frac{t}{(R_1+R_2)C}}(1)$$ for some constants a and b and by comparing this with the equation you give for current, I decided my conclusion.
 
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  • #7
If there was zero initial charge on the capacitor, then the current magnitude at t=0 would be 36 ÷ 14 amps. But we are told the current is a spike or pulse of magnitude 9 A peak at t=0. So we conclude there must be some initial charge on the capacitor in order to give a total loop voltage at t=0 of 9 ×14 volts.

If you set up and solve the 1st order D.E. this should be confirmed.
 
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Related to RC-RL Circuit: Solving for Capacitance Value

1. What is an RC-RL circuit?

An RC-RL circuit is a type of electrical circuit that contains both a resistor (R) and a capacitor (C) in series, and a resistor (R) and an inductor (L) in parallel. This type of circuit is commonly used in electronic devices to control the flow of electricity.

2. How do you solve for the capacitance value in an RC-RL circuit?

To solve for the capacitance value in an RC-RL circuit, you can use the formula C = τ/R, where C is the capacitance value, τ is the time constant (equal to L/R), and R is the resistance value. You can also use the equation Q = CV, where Q is the charge stored in the capacitor and V is the voltage across the capacitor.

3. What is the time constant in an RC-RL circuit?

The time constant in an RC-RL circuit is a measure of how quickly the capacitor charges or discharges. It is equal to the product of the resistance (R) and the capacitance (C), or τ = RC. The time constant is important because it determines the rate at which the circuit reaches its steady-state condition.

4. How does the value of the inductor affect the capacitance in an RC-RL circuit?

The value of the inductor (L) in an RC-RL circuit affects the capacitance value by changing the time constant (τ). A larger inductance value will result in a longer time constant, which means the capacitor will take longer to charge or discharge. This can also affect the overall behavior and stability of the circuit.

5. What are some practical applications of RC-RL circuits?

RC-RL circuits have a variety of practical applications, including in electronic filters, power supplies, and audio amplifiers. They are also commonly used in electronic devices such as radios, televisions, and computers. Additionally, RC-RL circuits are important in understanding the behavior of more complex circuits and systems.

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