What is the main application of RC circuits?

They are widely used as filters (low-pass, high-pass) and for timing applications (delays, oscillators like 555 timer). When in a circuit you need to control the order of events, RC circuits are often employed.

How does the capacitor affect the circuit?

It stores energy in an electric field, opposing changes in voltage. This creates a time delay between input and output changes. This principle is fundamental for timing and filtering applications.

What is the significance of the RC time constant (τ)?

The RC time constant (τ) indicates how quickly a capacitor charges or discharges through a resistor. It is defined as the product of resistance (R) and capacitance (C). After one time constant, the capacitor charges to about 63% of the supply voltage, and after five time constants, it is nearly fully charged or discharged.

What happens after 5 time constants (5τ)?

The capacitor is considered fully charged (or discharged), reaching approximately 99.3% of its final value.

Why do my resistors break in RC circuits?

Excessive power dissipation can cause resistors to overheat and fail. Note that during the initial instants of capacitor loading, it behaves like a short circuit, meaning that current will be very high..

Graphic calculator of RC circuit and time constant

How to use the graphic calculator of RC circuit and time constant

To use the calculator enter three values. The blank field will automatically be calculated. If you fill in all three fields, the last calculated value will be recalculated. You can modify the units using the selectors.

Understanding the RC circuit

An RC circuit consists of a power supply, a resistor and a capacitor in series. The capacitor ends up being charged at the same voltage value as the power supply. This, by itself, doesn't seem particularly interesting. The key is that, by properly selecting the value of R and C, we can choose when the capacitor will be charged. Being able to control time means being able to control the sequence in which things happen in an electrical circuit. This is why RC circuits are so important. In the figure below you can see the basic shape of this circuit. Note that in the figure, there is a switch between the source and R. This switch indicates that the source is, first, disconnected from the circuit (and, therefore, the capacitor discharged), and is connected at a given moment, from which the capacitor begins to charge. This representation is conceptual. In reality, what usually happens is that the source is turned OFF and is switched ON at a specific time. The transition from OFF to ON is equivalent to the source being on and the switch going from open to closed. By the way, this circuit is also used to make low-pass filters, which are also key in electronics. It makes a lot of sense that they are related. Think about the following: with the RC circuit we manage to charge the capacitor with a delay with respect to power supply switch ON, we can intuitively understand that it is a circuit that reacts slowly to changes in its input. That is, if the power supply is switched ON and OFF very fast, the capacitor does not have time to charge and discharge completely. It will be left with a voltage oscillating close to an intermediate value, which will be higher or lower depending on the speed at which the source is turned on and off. We are not going to deviate any further from the initial topic, I leave you a link to the low-pass filter calculator, where you will find more information. Let's go back to the RC timer and look at it in detail.

Low pass filter

To understand how the RC circuit works, you have to understand two things: Ohm's Law, and the behavior of an ideal capacitance. Regarding Ohm's law, you have information on its corresponding calculator. ( Ohm's law ) and about the behavior of a capacitance with respect to its voltages and currents, we discussit here. The main characteristic of a capacitor is that the current that passes through it, is proportional to the variation of its voltage. Be careful, watch out! It is not proportional to the voltage, but to the variation of it. Therefore, you can imagine that if there is no voltage variation, the current will be 0. If the voltage varies very quickly, then the current will be very high. One thing that should stick in your mind: the voltage of a capacitor cannot vary instantaneously, as that would imply infinite current. I leave you the equation here, but with the aforementioned concept it already works for us.

$$ I = C \frac{dV}{dt} $$

Mathematically, it is said that the current is proportional to the derivative of the voltage. We have briefly discussed what happens if the voltage varies too quickly or too slowly. There is another interesting case that you have to keep in mind. What would happen if the tension varied constantly? Easy: its current would be constant. You can interpret this 'the other way around': if you put a constant current through the capacitor (say, 1A, just to have a number in your head), its voltage will grow constantly. That is, it will start at 0V, then 1V, 2V... And so on until the current stops or the capacitor explodes.

Well, we now know how a capacitor behaves. Now it remains to understand how the complete circuit behaves. Imagine that the switch is open (or the power supply is OFF, at 0V), and the capacitor is discharged (0V). At a given moment, the switch is closed (or the power supply is turned ON). Just when that happens, at the initial instant, a current begins to flow. By Ohm's Law, this current is determined by the value of the voltage source and the resistance (I remind you that the capacitor is completely discharged). As current passes through the capacitor, its voltage increases. Here the question we have to ask ourselves is: How does it increase? Well, at the initial moment, we went from having no voltage (the capacitor was discharged at 0V) to having some voltage. That is, there has been a variation in voltage. This variation is, at first, large, since the current was large as it was limited only by the R. Consequence: the capacitor voltage increases considerably. But of course, when the voltage at the capacitor increases, the current has to decrease, since the voltage difference on both sides of the R is now smaller. If the current decreases, the voltage variation also decreases. That is, the voltage continues to grow, but more slowly. This process is continuous. In the end, the current is so low that the voltage variation is also very low, until reaching a stable state, in which there is no current or voltage variation. If you use the calculator you can see this easily. On the left of the graph, the voltage is rising rapidly and the current is at a maximum. As time passes, the current decreases, and so does the variation in voltage. I take this opportunity to emphasize that what decreases is not the voltage, but the variation in voltage. This phenomenon has the following mathematical appearance:

$$ V_c(t) = V_{in}(1-e^\frac{-t}{RC}) $$

RC time constant (or τ (tau))

After having seen the 'way' in which the capacitor voltage will evolve, we must comment on how long it will take to do so. This is the key part, since we use this type of circuit to 'count' time. This time is determined by the product R x C. This multiplication is called time constant, and is usually expressed in summary with the Greek letter Tau (τ), which looks like a 't', but it is not. It's unintuitive, but if you multiply resistance by capacitance, that is, Ohms (Ω) times Farads (F), you get seconds (s).

The time constant allows you to 'move' yourself very quickly (just multiply R x C) on the capacitor voltage curve. In the figure above you can see it. For example, 1T (one Tau) is equivalent to the capacitor being charged to approximately 63%. 3T is equivalent to 95%, and 5T is slightly higher than 99%.

RC Circuit LTSpice Simulation

Download this LTSpice simulation to analyze the charging and discharging of an RC circuit. You can modify the R and C values to see how they affect the time constant and the charging curve of the capacitor. This is a great way to visualize and understand the behavior of RC circuits in practice. Also you can add parasitic elements to see how they affect the circuit's performance as they would do on a real board.

Download RC Circuit Simulation (.asc)

Frequently Asked Questions

What is the main application of RC circuits?
They are widely used as filters (low-pass, high-pass) and for timing applications (delays, oscillators like 555 timer). When in a circuit you need to control the order of events, RC circuits are often employed.
How does the capacitor affect the circuit?
It stores energy in an electric field, opposing changes in voltage. This creates a time delay between input and output changes. This principle is fundamental for timing and filtering applications.
What is the significance of the RC time constant (τ)?
The RC time constant (τ) indicates how quickly a capacitor charges or discharges through a resistor. It is defined as the product of resistance (R) and capacitance (C). After one time constant, the capacitor charges to about 63% of the supply voltage, and after five time constants, it is nearly fully charged or discharged.
What happens after 5 time constants (5τ)?
The capacitor is considered fully charged (or discharged), reaching approximately 99.3% of its final value.
Why do my resistors break in RC circuits?
Excessive power dissipation can cause resistors to overheat and fail. Note that during the initial instants of capacitor loading, it behaves like a short circuit, meaning that current will be very high..