Exploring the Lag of Voltage Across a Capacitor

In summary, the voltage across the capacitor (v0) lags vi because the capacitor voltage (V0) is 90 degrees behind the reference phase (I), while the voltage across the resistor (R) is in phase with the reference phase. This can be illustrated using a vector diagram, where Vi is shown to lead V0. An intuitive explanation is that the capacitor acts as a low-pass filter, causing a delay in the voltage across it compared to the voltage across the resistor.
  • #1
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Homework Statement



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


Homework Equations





The Attempt at a Solution


 

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  • #2
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.
 
  • #3
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.
 

1. What is a capacitor and how does it work?

A capacitor is an electrical component that stores and releases electrical energy. It is made up of two conducting plates separated by an insulating material called a dielectric. When a voltage is applied to the capacitor, it stores electrical charge on its plates. This stored charge can then be released when needed.

2. Why does a capacitor cause a lag in voltage?

A capacitor causes a lag in voltage because of its ability to store and release charge. When a voltage is applied to the capacitor, it takes time for the plates to charge up. Similarly, when the voltage is removed, the plates take time to discharge. This delay in charging and discharging leads to a lag in voltage across the capacitor.

3. How is the lag of voltage across a capacitor measured?

The lag of voltage across a capacitor can be measured by using an oscilloscope. The oscilloscope displays the voltage across the capacitor over time, allowing us to see the delay in the charging and discharging of the capacitor. The lag can also be calculated using the time constant formula, which involves the capacitance of the capacitor and the resistance in the circuit.

4. What factors affect the lag of voltage across a capacitor?

The lag of voltage across a capacitor is affected by several factors, including the capacitance of the capacitor, the resistance in the circuit, and the frequency of the voltage being applied. A higher capacitance or lower resistance will lead to a longer lag time. Similarly, a higher frequency will result in a shorter lag time.

5. How is the lag of voltage across a capacitor used in practical applications?

The lag of voltage across a capacitor is used in various practical applications, such as in AC circuits to control the flow of current. Capacitors are also used in electronic devices to store electrical energy and provide a stable voltage supply. In addition, the lag of voltage across a capacitor is used in filters to block certain frequencies and pass others, making it a crucial component in many electronic systems.

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