all about physics: RC Circuit, Charging and Discharging Capacitor

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In this post, we will talk about RC CIRCUITS. What is RC Circuit actually?

RC Circuits

An RC circuit is a circuit with both a resistor (R) and a capacitor (C). RC circuits are freqent element in electronic devices. They also play an important role in the transmission of electrical signals in nerve cells.

A capacitor can store energy and a resistor placed in series with it will control the rate at which it charges or discharges. This produces a characteristic time dependence that turns out to be exponential. The crucial parameter that describes the time dependence is the "time constant" R C .

We will confine our studies to the following circuit, in which the switch can be moved between positions a and b.

Let us begin by reviewing some facts about capacitors:

The charge on a capacitor cannot change instantaneously. The current is given by I = DQ / Dt. Hence the change in charge DQ = I Dt goes to zero as the time interval Dt goes to zero.

The current flowing into a capacitor in the steady state that is reached after a long time interval is zero. Since charge builds up on a capacitor rather than flowing through it, charge can build up until the point that the voltage V=Q/C balances out the external voltage pushing charge onto the capacitor.

When a capacitor of capacitance C is in series with a battery of voltage V_b and a resistor of resistance R, the voltage drops must be:

which is a statement that the voltage gained going across the battery must equal the voltage drop across the capacitor plus the voltage drop across the resistor. An equation where the rate of change of a quantitity (DQ/Dt) is proportional to the quantity (DQ) will always have an exponential solution. We consider two instances:

Discharging the capacitor: The capacitor initially is connected (switch in position a) for a long time, and is then disconnected by moving the switch to b at time t = 0. The capacitor then discharges, leaving the capacitor without charge or voltage after a long time.
Charging the capacitor: The switch is in position b for a long time, allowing the capacitor to have no charge. At time t = 0, the switch is changed to a and the capacitor charges.