Why Does the Voltage Across a Capacitor Lag Behind the Input Voltage?

  • Thread starter Thread starter p75213
  • Start date Start date
  • Tags Tags
    Capacitor Voltage
Click For Summary
SUMMARY

The voltage across a capacitor (V0) lags the input voltage (Vi) by 90 degrees due to the phase relationship between current and voltage in an AC circuit. In this discussion, the reference phase is set at 0 degrees for the current (I), which is in phase with the voltage across the resistor (R). The analysis demonstrates that while the voltage across the resistor is in phase with the current, the capacitor voltage lags behind the current, resulting in Vi leading V0. This relationship is confirmed through vector diagrams and is foundational in understanding AC circuit behavior.

PREREQUISITES
  • Understanding of AC circuit theory
  • Familiarity with vector diagrams in electrical engineering
  • Knowledge of phase relationships in electrical components
  • Basic calculus and differential equations
NEXT STEPS
  • Study the concept of impedance in AC circuits
  • Learn about phasor representation of AC voltages and currents
  • Explore the relationship between capacitors and inductors in AC circuits
  • Investigate the use of differential equations in circuit analysis
USEFUL FOR

Electrical engineering students, circuit designers, and anyone interested in understanding the dynamics of AC circuits and the behavior of capacitors in relation to input voltages.

p75213
Messages
93
Reaction score
0

Homework Statement



Can somebody explain why the voltage across the capacitor (v0) lags vi?


Homework Equations





The Attempt at a Solution


 

Attachments

  • ScreenHunter_01 Jan. 22 13.00.gif
    ScreenHunter_01 Jan. 22 13.00.gif
    2.3 KB · Views: 534
Physics news on Phys.org
I proved it with a vector diagram.
Let I be the reference phase ie. 0 degrees. Because the voltage across R is in phase with I it also has 0 phase.
The capacitor voltage V0 lags I by 90 degrees ie. -90
Vi=V0+Rvoltage.
This shows Vi vector after I (R voltage) but before V0.
Therefore Vi leads V0.

I still would appreciate a more intuitive explanation if somebody has one.
 
My old ARRL handbook explained this in a non-calculus way. I never bothered to try to understand it. It was obvious to me once I had diff eq's and transform techniques - meanwhile, I believe yours is the best intuitive explanation there is.
 

Similar threads

Engineering Voltage in capacitors within an Energy Harvester
  • · Replies 4 ·
Replies
4
Views
2K
Power System Fault Phasor Diagram
  • · Replies 15 ·
Replies
15
Views
3K
Find the Capacitance when given the Power Factor
  • · Replies 4 ·
Replies
4
Views
2K
Engineering How Does a Capacitor Affect Ripple Voltage in a Diode Circuit?
  • · Replies 15 ·
Replies
15
Views
7K
Is the Formula for Voltage Drop Across Capacitor Opposite of Resistor?
  • · Replies 5 ·
Replies
5
Views
3K
Engineering RC Circuit/Node voltage question
  • · Replies 3 ·
Replies
3
Views
3K
Engineering Calculating voltage across resistors/capacitors in a circuit
  • · Replies 4 ·
Replies
4
Views
2K
Calculating the voltage across capacitors and resistors with switches
  • · Replies 2 ·
Replies
2
Views
1K
Infinite current required to change capacitor voltage instantaneously?
  • · Replies 2 ·
Replies
2
Views
2K
Does a capacitor delay the voltage from a voltage source in a circuit?
  • · Replies 10 ·
Replies
10
Views
3K