# How Do You Calculate Capacitance in a DC Circuit with a Fully Charged Capacitor?

• Lambda96
In summary, the circuit looks like this: There is a resistor, ##R##, and a capacitor, ##C##. The resistor has the value of ##100 \Omega## and the capacitor has the value of ##9.7 \cdot 10^{-4}F##.
Lambda96
Homework Statement
What does the circuit look like and what are the values of resistor ##R## and capacitance ##C##?
Relevant Equations
none
Hi,

I am not sure if I have calculated the task correctly

I have now assumed that the capacitor does not need to be charged and is therefore fully charged. In a DC circuit, a capacitor acts like an infinitely large resistor or like an open switch, so I assumed that it is a parallel circuit and that it looks like this.

The resistor then has the following value ##R=100 \Omega##.

Using the impedance and the value for ##R##, I can then calculate the value for ##C##.

The value for the impedance in parallel circuit is

$$|Z|=\frac{1}{\sqrt{R^-2+\omega^2 C^2}}$$

##C## can then be calculated as follows

$$C=\frac{R^2-Z^2}{R \omega z}$$

If I now substitute all the values into the above formula, I get the following ##C=9.7 \cdot 10^{-4}F##.

Lambda96 said:
ƒHomework Statement: What does the circuit look like and what are the values of resistor ##R## and capacitance ##C##?
Relevant Equations: none

Hi,

I am not sure if I have calculated the task correctly

View attachment 327711
I have now assumed that the capacitor does not need to be charged and is therefore fully charged. In a DC circuit, a capacitor acts like an infinitely large resistor or like an open switch, so I assumed that it is a parallel circuit and that it looks like this.

View attachment 327712

The resistor then has the following value ##R=100 \Omega##.

Using the impedance and the value for ##R##, I can then calculate the value for ##C##.

The value for the impedance in parallel circuit is

$$|Z|=\frac{1}{\sqrt{R^-2+\omega^2 C^2}}$$

##C## can then be calculated as follows

$$C=\frac{R^2-Z^2}{R \omega z}$$

If I now substitute all the values into the above formula, I get the following ##C=9.7 \cdot 10^{-4}F##.
It looks like you used frequency, ƒ, rather than angular frequency. Remember, ##\omega=2\pi f ## .

LaTeX tip:
To write ##R^{-2}## rather than ##R^-2##, place the ##-2## in braces { }, e.g. ##\{ -2 \}## .

Lambda96 and berkeman
Thanks SammyS for your help and for looking over my calculation, thanks also for the tip on how to write ##R^{-2}## in latex

You are right, unfortunately I used the frequency of ##50Hz## in the calculation instead of ##\omega=2 \pi 50Hz##. Then the result for ##C## is as follows, ##C=0.015 F##

Lambda96 said:
Thanks SammyS for your help and for looking over my calculation, thanks also for the tip on how to write ##R^{-2}## in latex

You are right, unfortunately I used the frequency of ##50Hz## in the calculation instead of ##\omega=2 \pi 50Hz##. Then the result for ##C## is as follows, ##C=0.015 F##
The decimal point is in the wrong place.

Lambda96

## What is an unknown circuit in a black box?

An unknown circuit in a black box refers to an electrical circuit whose internal components and configuration are not visible or known to the observer. The term "black box" signifies that the internal workings are hidden, and the only way to understand the circuit is through external testing and analysis.

## How can you determine the components inside a black box circuit?

To determine the components inside a black box circuit, you can perform a series of electrical tests such as measuring voltage, current, and resistance at various points. Techniques like applying known signals and observing the output responses, using an oscilloscope, and employing network analysis methods can help infer the internal components and their configurations.

## What tools are commonly used to analyze a black box circuit?

Common tools used to analyze a black box circuit include multimeters for measuring voltage, current, and resistance; oscilloscopes for observing signal waveforms; signal generators for applying test signals; and sometimes more advanced equipment like network analyzers and spectrum analyzers to study the circuit's behavior in the frequency domain.

## What are the challenges in analyzing a black box circuit?

The challenges in analyzing a black box circuit include the inability to directly observe the internal components, the complexity of the circuit, potential non-linear behavior, and the presence of unknown or proprietary components. Additionally, without a schematic, it can be difficult to determine the exact configuration and interactions between components.

## Why is it important to understand a black box circuit?

Understanding a black box circuit is important for troubleshooting, reverse engineering, and ensuring compatibility with other systems. It can also be crucial for validating the circuit's performance, identifying potential faults or weaknesses, and for educational purposes to learn about circuit behavior and design principles.

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