Calculate Frequency of RLC Series Circuit with R=1kOhms, L=100mH, C=1uF

Click For Summary
SUMMARY

The discussion focuses on calculating the frequency of an RLC series circuit with resistance R = 1 kOhm, inductance L = 100 mH, and capacitance C = 1 µF, at which the current lags the supply voltage by 45 degrees. The impedance is defined by the formula Z = √(R² + (ωL - 1/ωC)²) and the phase angle is determined using arctan[(ωL - 1/ωC) / R]. By setting the condition for a 45-degree phase shift, the relationship tan(θ) = (X_L - X_C) / R leads to the conclusion that the circuit can be analyzed with one equation and one unknown frequency, allowing for the calculation of both frequency and impedance.

PREREQUISITES
  • Understanding of RLC circuit theory
  • Familiarity with impedance calculations
  • Knowledge of phase angles in AC circuits
  • Basic algebra for solving equations
NEXT STEPS
  • Study the derivation of impedance in RLC circuits
  • Learn about the relationship between frequency and phase angle in AC circuits
  • Explore the use of complex numbers in circuit analysis
  • Investigate the effects of varying R, L, and C on circuit behavior
USEFUL FOR

Electrical engineers, students studying circuit theory, and anyone involved in the design or analysis of RLC circuits will benefit from this discussion.

jayhar
Messages
1
Reaction score
0
Given that R = 1 kOhms, L=100mH and C = 1uF, calculate the frequency at which the current in the circuit lags the supply voltage by 45deg.

Show how the impedance of the circuit is given by Z = sqr root R2 + (wL - 1/wC)2
arctan [(wL - 1/wC) / R]

I have not been given any information regarding supply voltages or frequencies.
I can not see how i can calculate impedance with no frequencies.

I am assuming for Q1 that tan theta = XL-XC/R, this can only be 1000/1000 = 1 = 45deg.
 
Physics news on Phys.org
You already have that [tex]X_L - X_C = 1000[/tex]
Write the impedances as functions of L and C (known) and the frequency (unknown).
You have one equation with one unknown, so you can calculate it.
Use the calculated frequency to obtain the impedance.
 

Similar threads

Phase difference RLC circuit
  • · Replies 5 ·
Replies
5
Views
3K
Series RLC Circuits: Resonant Frequency of 60° at 40 Hz
  • · Replies 8 ·
Replies
8
Views
3K
Current flowing through resistor in RLC circuit (C in parallel with L)
  • · Replies 19 ·
Replies
19
Views
3K
Engineering AC Source driving an RLC circuit....
  • · Replies 5 ·
Replies
5
Views
2K
If R^2= L/C, show the total power is independent of frequency
  • · Replies 5 ·
Replies
5
Views
2K
Engineering RLC circuit with two angular frequencies
  • · Replies 1 ·
Replies
1
Views
2K
Resonant frequency of L - R||C circuit
  • · Replies 21 ·
Replies
21
Views
2K
Engineering Q of RLC circuit, confused with provided answer
  • · Replies 1 ·
Replies
1
Views
1K
Engineering RLC Series Network: Impedance, Current, Power Factor, Phasor Diagram
  • · Replies 20 ·
Replies
20
Views
5K
Engineering Quality factor and freq bandwidth in a series RLC circuit
  • · Replies 2 ·
Replies
2
Views
3K