Calculate the impedance in this RC circuit

In summary, impedance in an RC circuit is the total opposition to the flow of current and is a combination of resistance and reactance. It can be calculated using the formula Z = √(R^2 + Xc^2) and is affected by the resistance, capacitance, and frequency. The current in an RC circuit is inversely proportional to the impedance, and in an RC circuit, the voltage and current are out of phase by 90 degrees.
  • #1
joelkato1605
19
2
Homework Statement
By calculating impedance, find the amplitude and phase of the current flowing in the
RC circuit shown below (Figure 3.1
Relevant Equations
Z =sqrt[ R^2 + (1/wc )^2]

I=v/Z
1618839771455.png

So Z = sqrt[ R^2 + (1/wc )^2] and V=Ecos(wt) so I= Ecos(wt) / sqrt[ R^2 + (1/jwc )^2] but how do I use this to find the amplitude and phase of the current?
 

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  • #2
Hi,

Are you familiar with working with complex numbers ?

##\ ##
 
  • #3
yeah I've done a bit on them
 
  • #4
Can you write the impedance as a complex number (not only its modulus)?
 
  • #5
https://www.electrical4u.com/rc-circuit-analysis/#:~:text=An%20RC%20circuit%20is%20defined,RL%20circuit%20or%20RLC%20circuit.
 

1. What is the definition of impedance in an RC circuit?

Impedance in an RC circuit is the measure of the opposition that the circuit presents to the flow of alternating current (AC). It is a combination of resistance and reactance, where reactance is the opposition to the flow of AC due to the capacitance of the circuit.

2. How do you calculate the impedance in an RC circuit?

The impedance in an RC circuit can be calculated using the formula Z = √(R^2 + Xc^2), where R is the resistance in the circuit and Xc is the reactance due to the capacitance. The reactance can be calculated using the formula Xc = 1/(2πfC), where f is the frequency of the AC and C is the capacitance of the circuit.

3. What factors affect the impedance in an RC circuit?

The impedance in an RC circuit is affected by the resistance, capacitance, and frequency of the AC. A higher resistance will result in a higher impedance, while a higher capacitance or frequency will result in a lower impedance.

4. How does the impedance affect the behavior of an RC circuit?

The impedance in an RC circuit affects the flow of current and voltage in the circuit. A higher impedance will result in a lower current and voltage, while a lower impedance will result in a higher current and voltage. It also affects the phase relationship between the current and voltage, with a higher impedance resulting in a larger phase difference.

5. What is the significance of calculating the impedance in an RC circuit?

Calculating the impedance in an RC circuit is important for understanding the behavior and performance of the circuit. It helps in designing and optimizing the circuit for specific applications, such as filtering or signal processing. It also allows for troubleshooting and identifying any issues or malfunctions in the circuit.

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