# Equivalent resistance with a capacitor

• RED119
In summary, the student is trying to find the equivalent resistance for a circuit with a capacitor. The student is not sure how to calculate equivalent resistance when there is a capacitor in the circuit. The student is asking for help to find the equivalent resistance.
RED119

## Homework Statement

So I need to find the equivalent resistance for the following RC circuit to calculate the time constant, but I got stuck in terms of finding out the equivalent resistance.

V = IR

## The Attempt at a Solution

So the thing I am not sure on is how do you calculate equivalent resistance when there is a capacitor in there? it counts as an element right? so the resistors are in neither series or parallel? or is there a way to calculate the equivalent resistance and I am just missing it? cause the resistors don't share two common but separate nodes with the capacitor in there

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The basic procedure is to remove the capacitor from the circuit, then find the Thevenin Equivalent of the remaining network as seen from the terminals where the capacitor was formerly connected. The resistance that the capacitor "sees" is the Thevenin resistance.

If you haven't done Thevenin Equivalents yet, the essential idea is to replace the voltage source with a short circuit (an open circuit if it were a current source instead) and find the equivalent resistance at the terminals where the capacitor was connected.

gneill said:
The basic procedure is to remove the capacitor from the circuit, then find the Thevenin Equivalent of the remaining network as seen from the terminals where the capacitor was formerly connected. The resistance that the capacitor "sees" is the Thevenin resistance.

If you haven't done Thevenin Equivalents yet, the essential idea is to replace the voltage source with a short circuit (an open circuit if it were a current source instead) and find the equivalent resistance at the terminals where the capacitor was connected.
So do something like one of these? I don't totally understand how that will make it so you can find an equivalent resistance

So i think you are saying take out the capacitor in the second drawring, and have the two resistors be connected and then they are in parallel and that's the thevenin resistance?

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Replace the voltage source with a short circuit (a piece of wire).

gneill said:
Replace the voltage source with a short circuit (a piece of wire).
so that would make the 10k in this example shorted?

RED119 said:
so that would make the 10k in this example shorted?
It would indeed.

gneill said:
It would indeed.
so the equivalent resistance is just 50k? Why is the 10k shorted, or at least the capacitor sees is that way? logically speaking it seems like it should dissipate power from the battery with its placement, and have a voltage drop across it...

RED119 said:
so the equivalent resistance is just 50k? Why is the 10k shorted, or at least the capacitor sees is that way? logically speaking it seems like it should dissipate power from the battery with its placement, and have a voltage drop across it...
Yes, but the capacitor never "sees" that resistor. The voltage source being fixed, creates an impenetrable wall beyond which no voltage changes in the rest of the circuit can pass. The battery can supply all the current that that resistor will use.

CWatters
gneill said:
Yes, but the capacitor never "sees" that resistor. The voltage source being fixed, creates an impenetrable wall beyond which no voltage changes in the rest of the circuit can pass. The battery can supply all the current that that resistor will use.
that makes sense, so its almost like a sub-circuit that has no affect on the capacitor. Thanks so much for the help and explanations

CWatters
Yup. If you wish to picture it another way, the voltage source can be duplicated and produces the same potential for both "sides" of the circuit:

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CWatters
Are you sure you drew the schematic correctly? It's an unusual question because the 10K resistor is meaningless in the analysis, as others have described.

DaveE said:
Are you sure you drew the schematic correctly? It's an unusual question because the 10K resistor is meaningless in the analysis, as others have described.
I think that was one of the points the question was trying to get across.
Another point was the concept of an ideal voltage source, having zero internal resistance, could consequently be replaced with a short to find the equivalent, Thevenin, circuit.

gneill

## 1. What is equivalent resistance with a capacitor?

Equivalent resistance with a capacitor refers to the effective resistance of a circuit that contains a capacitor. It takes into account both the actual resistance of the circuit and the reactance of the capacitor, which is dependent on the frequency of the current.

## 2. How is equivalent resistance with a capacitor calculated?

The equivalent resistance with a capacitor is calculated by taking the square root of the sum of the squared values of the actual resistance and the reactance of the capacitor. The reactance can be calculated using the formula Xc = 1/(2πfC), where f is the frequency and C is the capacitance of the capacitor.

## 3. Why is equivalent resistance with a capacitor important?

Equivalent resistance with a capacitor is important because it helps us to understand the behavior of circuits that contain capacitors. It allows us to determine the total resistance of the circuit and how it will affect the flow of current. This information is crucial in designing and analyzing electronic circuits.

## 4. How does equivalent resistance with a capacitor affect the time constant of a circuit?

The time constant of a circuit is affected by the equivalent resistance with a capacitor. A higher equivalent resistance will result in a longer time constant, meaning that it will take longer for the capacitor to fully charge or discharge. This can affect the overall performance of the circuit and must be taken into consideration in circuit design.

## 5. Can equivalent resistance with a capacitor be negative?

No, equivalent resistance with a capacitor cannot be negative. It is always a positive value that represents the total resistance of the circuit. The only way to have a negative resistance in a circuit is if there is a negative resistance component, which is not possible with a capacitor.

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