Understanding RC Circuit Behavior in Excel: Exploring Energy and Current Changes

In summary, the conversation discusses a problem with calculating the total energy delivered in a circuit using various equations, including v(t), i(t), E, and P. The issue is resolved by multiplying each power value by the timestep size and taking into account the initial current of 6A due to the voltage source switching from 12V to 0V. The initial current is not 0A because the capacitor can change its current instantaneously.
  • #1
sad panda
3
0

Homework Statement



ULchw.png

Homework Equations


v(t) = v0*e^(-t/RC)
i(t) = C*(dv/dt)
E = .5*C*V^2
P=v*i

The Attempt at a Solution


I'm having trouble with part e. As far as I can tell, all of my equations are correct, but the total energy delivered is notably less than the initial energy; I was hoping someone could point out my mistake.
Here's what I've got:
EVFVw.png

eUIqJ.png
 
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  • #2
I can see a few odd things. First, the initial current should be 6A. If you're trying to use i = C*dv/dt to calculate it you'll need a dV value, the change in voltage over the timestep, not the current value of V. And you'll need to use dt, not [itex]\tau[/itex]. But then, why not write an explicit formula for the current as you did for the voltage? i(t) = Io exp(-t/[itex]\tau[/itex]).

The sum of the instantaneous power over time is not the total power delivered. Each of those power points needs to be multiplied by the timestep size to determine the energy delivered in that timestep. So for the timesptep at time t, the energy delivered is approximately v(t)*i(t)*dt.
 
  • #3
Thank you very much for the response. I seem to be getting the correct answer (~1.845 J which is within my allowed margin of error) now when each power value is multiplied by dt. However, I'm a bit confused as to why the initial current would be 6A, why is it not the steady state value of 0A?
 
  • #4
sad panda said:
Thank you very much for the response. I seem to be getting the correct answer (~1.845 J which is within my allowed margin of error) now when each power value is multiplied by dt. However, I'm a bit confused as to why the initial current would be 6A, why is it not the steady state value of 0A?

If I understood the circuit properly, at time t=0 the voltage source switches from supplying 12V to supplying 0V, or in other words, it becomes a short circuit. This being so, the capacitor is left charged up with 12V on it, and that 12V "sees" a resistance of 2.0 Ohms. 12V/2Ω = 6.0 Amps. That's your initial current.
 
  • #5
gneill said:
If I understood the circuit properly, at time t=0 the voltage source switches from supplying 12V to supplying 0V, or in other words, it becomes a short circuit. This being so, the capacitor is left charged up with 12V on it, and that 12V "sees" a resistance of 2.0 Ohms. 12V/2Ω = 6.0 Amps. That's your initial current.

Thanks, that makes sense. I forgot that the current through a capacitor can change instantaneously.
 

1. How do I create an RC circuit in Excel?

To create an RC (resistor-capacitor) circuit in Excel, you will need to use the built-in functions for resistors and capacitors, as well as the circuit builder tool. First, use the "Resistor" and "Capacitor" functions to input the values for each component. Then, use the circuit builder tool to connect the components and create the circuit.

2. How do I input the values for the components in the RC circuit?

You can input the values for the resistor and capacitor using the respective functions in Excel. For example, to input a resistor with a value of 100 ohms, you would use the function "=Resistor(100)". Similarly, to input a capacitor with a value of 10 microfarads, you would use the function "=Capacitor(10E-6)".

3. What is the purpose of solving an RC circuit in Excel?

Solving an RC circuit in Excel allows you to analyze the behavior of the circuit and calculate important parameters such as voltage, current, and time constants. This can help in understanding the functionality of the circuit and making design decisions.

4. How do I calculate the time constant of an RC circuit in Excel?

To calculate the time constant of an RC circuit in Excel, you will need to use the formula "=RC_TimeConstant(R,C)" where R is the value of the resistor and C is the value of the capacitor. This function will return the time constant in seconds.

5. Can I simulate the behavior of an RC circuit in Excel?

Yes, Excel allows you to simulate the behavior of an RC circuit by using the "Solver" tool. This tool can be used to solve complex equations and find the values of variables that will satisfy a given condition. By setting up the circuit equations and using the "Solver" tool, you can simulate the behavior of the RC circuit and observe how the parameters change over time.

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