Question concerning capacitors

[WildStriker]

Does anyone know how you can work and calculate the value of a capacitor in an rc circuit if you have a resistor of 1 kilo ohm with a cut off frequency of, for example, 2.5 kHz?

Comments will be appreciated.

Thanks

 

[dknguyen]

Cutoff frequency is subject to how you define it. It tends to be simplified as a two-line graph with zero slope and then a ramped slope. In reality it is on continuous gradual curve. But traditionally, cutoff frequency -3dBi which is half the power (or 70.7% the magnitude). Then that is this formula:

f(Hz) = 1/(2*pi*RC)
radians(Hz) = 1/(RC)

 

[WildStriker]

Cutoff frequency is subject to how you define it. It tends to be simplified as a two-line graph with zero slope and then a ramped slope. In reality it is on continuous gradual curve. But traditionally, cutoff frequency -3dBi which is half the power (or 70.7% the magnitude). Then that is this formula:

f(Hz) = 1/(2*pi*RC)
radians(Hz) = 1/(RC)

I'm quite confused. The question is asking how I could calculate the value of the capacitor (C), required to meet the frequency response (2.5kHz)

Is this it, C=1/2*3.142*fR?

 

[MikeMl]

At the cutoff frequency, Xc = R
or 1/(2Π*2500*C) = 1000

I'll let you do the algebra.

 

[WildStriker]

At the cutoff frequency, Xc = R
or 1/(2Π*2500*C) = 1000

I'll let you do the algebra.

I'll try and rephrase the question for clarity,

If you have a low pass filter rc circuit (with a cut off frequency of 2.5kHz) with a 1 kilo ohm resistor, how do you theoretically calculate the value of the capacitor?

 

[MikeMl]

I'll try and rephrase the question for clarity,

If you have a low pass filter circuit diagram (with a cut off frequency of 2.5kHz) with a 1 kilo ohm resistor, how do you calculate the value of the capacitor required to meet the frequency response?

You solve the equation I gave you for C!!!! You can do that, right?

 

[Norlin]

At the cutoff frequency, Xc = R
or 1/(2Π*2500*C) = 1000

I'll let you do the algebra.

Using the equation provided and rearranging we get:
1/(2Π*2500*1000) = C

 

[WildStriker]

Using the equation provided and rearranging we get:
1/(2Π*2500*1000) = C

Okay I get it now I think.

I just used the calculator and it gave the answer 3927500. So what do you do next?

 

[Norlin]

Think your calculator is broken. Just looking at the equation one should be able to assume you're many orders of magnitude off.
funny, I get 63.366 nF

 

[WildStriker]

Think your calculator is broken. Just looking at the equation one should be able to assume you're many orders of magnitude off.
funny, I get 63.366 nF

I'm confused now. I did the equation again and it gave me 15700000. Is it okay if you can you walk me through your calculation on how you got 63.3 nF?

I followed the equation as 2*3.14*2500*1000 then divide 1.

 

[Norlin]

there's your problem, it's 1 divided by (2 * 3.14 * 2500 * 1000) and not the other way around
so this works out to 1 divided by 15707963.27

 

[WildStriker]

there's your problem, it's 1 divided by (2 * 3.14 * 2500 * 1000) and not the other way around
so this works out to 1 divided by 15707963.27

How does 2*3.14*2500*1000 = 15707963.27? I get 15700000. I still don't understand. And yes I took bodmas into account but my answer still differs.

I putted in on my calculator 1/(2X3.14X2500X1000) and gave me 6.3694267519

Sorry if I'm causing any trouble.

 

[Norlin]

2*pi*2500*1000 = 15707963.27

1 / (2*pi*2500*1000) = 63.366 nF

the reason you get 15700000 is because you're rounding pi to 3.14 and I get 15707963.27 because I am not rounding pi

either way makes little difference and you can probably use either number, with your number you get:
63.7 nF

with my number you get:
63.3 nF

your capacitor is going to have a % tolerance where the 0.4nF calculation difference isn't going to make a difference

 

[WildStriker]

2*pi*2500*1000 = 15707963.27

1 / (2*pi*2500*1000) = 63.366 nF

the reason you get 15700000 is because you're rounding pi to 3.14 and I get 15707963.27 because I am not rounding pi

either way makes little difference and you can probably use either number, with your number you get:
63.7 nF

with my number you get:
63.3 nF

your capacitor is going to have a % tolerance where the 0.4nF calculation difference isn't going to make a difference

Okay thanks.

One last question, when calculating the microfarad (uF) of the capacitor, do you still follow the samr formula?

 

[Norlin]

umm, micro, nano, pico, milli, etc...these are just standard unit prefixes. I'm sure you're familiar with millimeters, centimeters, meters and kilometers right? Basically that's just 1/1000 of a meter, 1/100 of a meter, 1/1 of a meter and 1000/1 of a meter right? Or in other words 1m * 10^-3 for millimeter (or mm). So a micrometer is 1/1000000 of a meter (10^-6 meter), or a micrometer is 1/1000 of a millimeter. A nanometer is 1/1000 of a micrometer and a picometer would be 1/1000 of a nanometer.
Here's one of hundreds of sites that explain unit prefixes: http://www.telecomabc.com/p/prefix.html