Calculating Current in a Series RC Circuit

In summary, the capacitor has a resistor and a voltage source. The voltage source is 10 volts and the current through the capacitor is 0.00062 Amps.
  • #1
IronaSona
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Hi , i was just wondering how would i find the current through a capacitor (Series RC circuit)

I found a questions online which asks to find the voltage and the current through a capacitor at 1kHz and 10Khz

Capacitor = 0.01uF
Resistor = 100 Ohms
Voltage Source = 10v
1.PNG

ive done some calculations but not sure they are 100% correct too
 
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  • #2
0.01 ##\mu##F is ##10^{-8}## F

##\ ##
 
  • #3
BvU said:
0.01 ##\mu##F is ##10^{-8}## F

##\ ##
so would it be 0.00062A across the capacitor ?
 
  • #4
IronaSona said:
I found a questions online which asks to find the voltage and the current through a capacitor at 1kHz and 10Khz
So my advice is: treat it as homework
  • Provide a complete problem statement ( Now we have to reconstruct this is about a RC series circuit -- from something you are not sure about )
  • list the relevant equations
  • clarify what the symbols used stand for
I'm not all that happy with the didactics of the treatment here but others may disagree.

You have

1625737029973.png

With (a bit much, but elementary): $$\begin{align*} V_0 &= |V_0| e^{j\omega t} \\ V_0 &= Z_{\text tot} I \\ Z_{\text tot} & = Z_R + Z_C \\V_C &= V_0 {Z_C\over Z_{\text tot}} \\
Z_R &= R\\Z_C &= {1\over j\omega C} \\V_C &= Z_C I\end{align*}$$
easy to solve, no reason for uncertainty.

However, I have assumed you are familiar with complex numbers - something I have to guess because it's not evident from your original post.

If you are not, I recommend picking it up:
BvU said:
I recall a short writeup by @LCKurtz title There’s nothing imaginary about complex numbers. It's more for teachers but there are similarities with Smith (like in Kurtz 3.1). It sure has the advantage of being al lot more concise !
Lynn's other writeup alternating current impedance is also quite good in your context.

(Smith is "The Scientist and Engineer's Guide to Digital Signal Processing")
##\ ##
 
Last edited:
  • #5
This is a sinusoidal steady state problem. For some reason you have calculated only the magnitude of the voltage and current and not the phase. Also, as others have mentioned 0.01uF = 10^-8 F. Not sure what is expected of you but since this is a series circuit just divide the voltage by the complex impedance which (at 1k Hz) in this case is just 100 - j * (1/(2*pi*10^3*10^-8)). That would be the current. The voltage would then be the current * (- j * (1/(2*pi*10^3*10^-8)). If you are just interested in magnitudes then of course take the square root of the sum of the square of the impedances and do the same thing.
 
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Related to Calculating Current in a Series RC Circuit

1. What is a series RC circuit?

A series RC circuit is a circuit that contains a resistor (R) and a capacitor (C) connected in series. This means that the current flows through the resistor and then through the capacitor, one after the other.

2. How do you calculate the total resistance in a series RC circuit?

The total resistance in a series RC circuit is calculated by adding the resistance of the resistor (R) and the reactance of the capacitor (XC). The formula for total resistance is Rtotal = R + XC = R + 1/(2πfC), where f is the frequency of the circuit and C is the capacitance of the capacitor.

3. What is the formula for calculating the current in a series RC circuit?

The formula for calculating the current in a series RC circuit is I = V/Rtotal, where I is the current, V is the voltage, and Rtotal is the total resistance in the circuit.

4. How does the current change over time in a series RC circuit?

In a series RC circuit, the current initially increases as the capacitor charges up. Once the capacitor is fully charged, the current decreases and eventually becomes zero as the capacitor acts as an open circuit. If the voltage source is removed, the capacitor will then discharge and the current will flow in the opposite direction until it reaches zero again.

5. How does the frequency affect the current in a series RC circuit?

The frequency of the circuit affects the reactance of the capacitor, which in turn affects the total resistance and therefore the current. As the frequency increases, the reactance of the capacitor decreases, resulting in a lower total resistance and a higher current. Likewise, as the frequency decreases, the reactance increases, resulting in a higher total resistance and a lower current.

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