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Back to [[Electricity_and_Magnetism]]
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  [[Electricity_and_Magnetism|⬅ Back to Electricity and Magnetism]]
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  [[Circuits RC|🌐 Version en français : Circuits RC]]
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<div style="border-left:5px solid #0ea5e9; padding:1em; background-color:#ecfeff; margin:0.75em 0 1em;">
  <p style="margin:0; font-weight:bold;">📘 RC Circuits</p>
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= Textbook =
= Textbook =
*[https://openstax.org/books/university-physics-volume-2/pages/10-5-rc-circuits University Physics Volume 2: Chapter 10.5 - RC Circuits]
 
<div style="border:1px solid #28a745; padding:0.8em; background-color:#f0fdf4; margin:1em 0;">
[https://openstax.org/books/university-physics-volume-2/pages/10-5-rc-circuits University Physics Volume 2: Chapter 10.5 - RC Circuits]
</div>


= What is a Capacitor and what is Capacitance =
= What is a Capacitor and what is Capacitance =
See [[Capacitors]]
See [[Capacitors]]


= RC Circuits =
= Theory =
 
== Capacitor Charging (Voltage over Time) ==
== Capacitor Charging (Voltage over Time) ==
[[File:Charging.png|right|400px]]
[[File:Charging.png|right|400px]]
During charging, the voltage across a capacitor increases exponentially, approaching its final value.
During charging, the voltage across a capacitor increases exponentially, approaching its final value.
<math> V(t) = V_0 \left( 1 - e^{-\frac{t}{RC}} \right) </math>
*Where:*
* *V(t)* is the voltage at time t (in volts, V)
* *V_0* is the final voltage (in volts, V)
* *R* is the resistance (in ohms, Ω)
* *C* is the capacitance (in farads, F)
* *t* is time (in seconds, s)


<div style="border-left:5px solid #0ea5e9; padding:0.8em 1em; background-color:#ecfeff; margin:1em 0;">
<math>V(t)=V_0\left(1-e^{-\frac{t}{RC}}\right)</math>
</div>
'''Where:'''
* <math>V(t)</math> is the voltage at time t (in volts, V).
* <math>V_0</math> is the final voltage (in volts, V).
* <math>R</math> is the resistance (in ohms, Ω).
* <math>C</math> is the capacitance (in farads, F).
* <math>t</math> is time (in seconds, s).
=== Charge ===
<div style="border-left:5px solid #0ea5e9; padding:0.8em 1em; background-color:#ecfeff; margin:1em 0;">
<math>q(t)=CV_0\left(1-e^{-\frac{t}{RC}}\right)</math>
</div>
=== Current ===
<div style="border-left:5px solid #0ea5e9; padding:0.8em 1em; background-color:#ecfeff; margin:1em 0;">
<math>i(t)=\frac{dq}{dt}=\frac{V_0}{R}e^{-\frac{t}{RC}}</math>
</div>
<br style="clear:both;" />


== Capacitor Discharge (Voltage over Time) ==
== Capacitor Discharge (Voltage over Time) ==
[[File:Discharging.png|right|400px]]
[[File:Discharging.png|right|400px]]
During the discharge of a capacitor through a resistor, the voltage decreases exponentially over time.
During the discharge of a capacitor through a resistor, the voltage decreases exponentially over time.
<math> V(t) = V_0 e^{-\frac{t}{RC}} </math>
 
*Where:*
<div style="border-left:5px solid #0ea5e9; padding:0.8em 1em; background-color:#ecfeff; margin:1em 0;">
* *V(t)* is the voltage at time t (in volts, V)
<math>V(t)=V_0e^{-\frac{t}{RC}}</math>
* *V_0* is the initial voltage (in volts, V)
</div>
* *R* is the resistance (in ohms, Ω)
 
* *C* is the capacitance (in farads, F)
'''Where:'''
* *t* is time (in seconds, s)
* <math>V(t)</math> is the voltage at time t (in volts, V).
* <math>V_0</math> is the initial voltage (in volts, V).
* <math>R</math> is the resistance (in ohms, Ω).
* <math>C</math> is the capacitance (in farads, F).
* <math>t</math> is time (in seconds, s).
 
=== Charge ===
 
<div style="border-left:5px solid #0ea5e9; padding:0.8em 1em; background-color:#ecfeff; margin:1em 0;">
<math>q(t)=CV_0e^{-\frac{t}{RC}}</math>
</div>
 
=== Current ===
 
<div style="border-left:5px solid #0ea5e9; padding:0.8em 1em; background-color:#ecfeff; margin:1em 0;">
<math>i(t)=\frac{dq}{dt}=-\frac{V_0}{R}e^{-\frac{t}{RC}}</math>
</div>
 
<br style="clear:both;" />


== Example Graphs ==
== Example Graphs ==
[[File:RC example graph.png|left|400px]]
[[File:RC example graph.png|left|400px]]
<br class="clear"/>
 
<div style="clear:both;"></div>
<br style="clear:both;" />


= Videos =
= Videos =
<youtube>vT6uonSYS9U</youtube>
<youtube>Fjzy6cHNn6w</youtube>


<div style="border-left:5px solid #ef4444; padding:0.8em 1em; background-color:#fff7f7; margin:1em 0;">
[https://www.youtube.com/watch?v=vT6uonSYS9U ▶ Watch video 1 on YouTube]
</div>
<div style="border-left:5px solid #ef4444; padding:0.8em 1em; background-color:#fff7f7; margin:1em 0;">
[https://www.youtube.com/watch?v=Fjzy6cHNn6w ▶ Watch video 2 on YouTube]
</div>


= Simulations =
= Simulations =
*[http://phet.colorado.edu/en/simulation/circuit-construction-kit-ac-virtual-lab PhET Circuit Construction Kit]
 
* [https://phet.colorado.edu/en/simulation/circuit-construction-kit-ac-virtual-lab PhET Circuit Construction Kit]
 
<br style="clear:both;" />




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= Other Links =
  [[Notes_on_DC_Circuits|⬅ Previous: DC Circuits]]
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  [[Magnetic Fields|Next: Magnetic Fields ➡]]
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Back to [[Electricity_and_Magnetism]]
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Next: [[Magnetic Fields]]

Latest revision as of 11:38, 31 October 2026

 ⬅ Back to Electricity and Magnetism



 🌐 Version en français : Circuits RC

📘 RC Circuits

Textbook

University Physics Volume 2: Chapter 10.5 - RC Circuits

What is a Capacitor and what is Capacitance

See Capacitors

Theory

Capacitor Charging (Voltage over Time)

During charging, the voltage across a capacitor increases exponentially, approaching its final value.

V(t)=V0(1−e−tRC)

Where:

  • V(t) is the voltage at time t (in volts, V).
  • V0 is the final voltage (in volts, V).
  • R is the resistance (in ohms, Ω).
  • C is the capacitance (in farads, F).
  • t is time (in seconds, s).

Charge

q(t)=CV0(1−e−tRC)

Current

i(t)=dqdt=V0Re−tRC


Capacitor Discharge (Voltage over Time)

During the discharge of a capacitor through a resistor, the voltage decreases exponentially over time.

V(t)=V0e−tRC

Where:

  • V(t) is the voltage at time t (in volts, V).
  • V0 is the initial voltage (in volts, V).
  • R is the resistance (in ohms, Ω).
  • C is the capacitance (in farads, F).
  • t is time (in seconds, s).

Charge

q(t)=CV0e−tRC

Current

i(t)=dqdt=−V0Re−tRC


Example Graphs


Videos

▶ Watch video 1 on YouTube

▶ Watch video 2 on YouTube

Simulations



 ⬅ Back to Electricity and Magnetism

 ⬅ Previous: DC Circuits

 Next: Magnetic Fields ➡


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