Physics Lesson 16.12.2 - A Short Recap on RC Circuits as a Useful Step to Understand the RL Circuits

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Welcome to our Physics lesson on A Short Recap on RC Circuits as a Useful Step to Understand the RL Circuits, this is the second lesson of our suite of physics lessons covering the topic of RL Circuits, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

A Short Recap on RC Circuits as a Useful Step to Understand the RL Circuits

In tutorial 15.7 "RC Circuits", we have explained that:

A RC circuit is the combination of a pure resistance R in ohms and a pure capacitance C in Farads. The capacitor stores energy while the resistor connected in series with the capacitor controls the charging and discharging process in the capacitor.

The equation which calculates the change in electric potential difference in terms of the time elapsed when charging a capacitor C through a resistor R, is

∆V(t) = ε ∙ (1 - e^{- t/R ∙ C})

where ε is the electromotive force generated by a DC source (for example a battery).

The charge stored in a capacitor as a function of time has a similar form, i.e.

Q(t) = Q₀ ∙ (1 - e^{- t/R ∙ C})

where Q(t) is the charge stored in a capacitor at any time instant t and Q₀ is the initial charge of the capacitor at the beginning of the charging process.

The R ∙ C term is usually denoted by τ (or τC); it has the unit of time and shows how fast the RC circuit is charging or discharging.

The discharge of a capacitor in a RC circuit is the inverse of charging process. In this case, we have a decreasing exponential function when considering the potential difference vs time variation. The equation of potential difference across a capacitor during the discharge process is

∆V(t) = ε ∙ e^{- t/R ∙ C}

and the charge remained in the capacitor at any instant during the discharge process, is

Q(t) = Q₀ ∙ e^{- t/R ∙ C}

Since the capacitance of a capacitor is

C = Q/∆V

and if we replace the potential difference ΔV with the electromotive force ε produced by the source (if we neglect the resistance of wire, then ΔV ≈ ε), we obtain for the charge stored in capacitor in terms of capacitance C:

Q(t) = C ∙ ε ∙ (1 - e^{- t/R ∙ C})

You have reached the end of Physics lesson 16.12.2 A Short Recap on RC Circuits as a Useful Step to Understand the RL Circuits. There are 5 lessons in this physics tutorial covering RL Circuits, you can access all the lessons from this tutorial below.

More RL Circuits Lessons and Learning Resources

Magnetism Learning Material
Tutorial ID	Physics Tutorial Title	Revision Notes	Revision Questions
16.12	RL Circuits
Lesson ID	Physics Lesson Title	Lesson	Video Lesson
16.12.1	What Are RL Circuits? An Overview
16.12.2	A Short Recap on RC Circuits as a Useful Step to Understand the RL Circuits
16.12.3	RL Circuits
16.12.4	What is the Dimension of τ?
16.12.5	What happens to the Current when the Source is removed from the Circuit

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