Unknown circuit in a black box

[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##.

 

[SammyS]

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]

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##

 

[SammyS]

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.

Simply divide your original answer by ##2\pi## .