[SOLVED] Capacitor Resistor in parallel

[HugeFanOfBadReligion]

Hey guys,

I have two resistors in series and to one of the resistor there is a capacitor connected in parallel. I have some questions about the current flowing in the circuit.


1. If i put a step voltage on the input, the current starts to flow through the first resistor and then it starts to charge the capacitor. Does that mean that in the very first moment during the voltage step the current flows only through the first resistor R1 to the ground? The current through the parallel resistor branch is therefor zero?

2. After some time the capacitor is charging exponentially. That means the voltage will change exponentially and so the current starts to flow in the parallel resistor branch also in exponential time course, am i correct?

3. If i will measure the total current in the node connected to the ground, will i observe the exponentially decaying current with some deviation from the mono-exponential function (due to the summation of the currents from both branches of my parallel network)?

4. what is the time constant of such decay? Is it just: tau=C1x(R1xR2/(R1+R2)) . Why not just C1xR2?

Thank you for your Answer

 

[LvW]

Answer to 4.):

For R2>> infinite, the time constant is R1*C1.
However, because the voltage across C1 is reduced by R2/(R1+R2) the final constant is the product

tau=R1*C1*R2/(R1+R2)=(R1||R2)*C1

 

[Venkadesh_M]

1, Yes there is no current or voltage on the R2 because there is no voltage in capacitor (both are parallel).
2, Correct the maximum voltage of the capacitor will be v1 / 2
3, Yes..
4, your supply voltage is V1 / 2 that is in series with R1||R2 to the capacitor (thevenines equivalent).. you can write the expression..

 

[HugeFanOfBadReligion]

Thank you guys, i was not sure about this, but now its much clearer.

Can you recommend me a free circuit simulator?
Do you know, whether any circuit simulator can provide the differential equations and the results needed to plot the simulated currents in the circuit?
I assume the software solves some diff. equations when it simulates the circuit, it would be of a great help if i could see the eqs.

thank you

 

[embeddedlover]

Forthe first point, we can't say current is completely zero, it is negligible..

 

[Venkadesh_M]

Forthe first point, we can't say current is completely zero, it is negligible..

What is the initial voltage of the capacitor when giving step input ? ?

 

[embeddedlover]

What is the initial voltage of the capacitor when giving step input ? ?

Yes, i agree with you at the instant of step input.. But he is asking when there is some current flow through R1. In that case definitely the voltage across cap is not zero.