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UExcel Physics: Study Guide & Test Prep18 chapters | 201 lessons | 13 flashcard sets

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Lesson Transcript

Instructor:
*David Wood*

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this lesson, you will be able to explain what an RLC series circuit is and use related equations to solve simple problems. A short quiz will follow.

On a basic level, the definition of an RLC series circuit is extremely simple. An **RLC series circuit** is a circuit where a battery, resistor (with resistance *R*), an inductor (with inductance *L*) and a capacitor (with capacitance *C*), RLC, are all connected in one complete loop (a series circuit). An RLC series circuit looks something like this. They're often used as tuning circuits in analogue radios and as low-pass, high-pass or band-pass filters when recording audio in a studio.

For an RLC circuit to operate, it also has to be an **alternating current** (or AC) circuit, which is where, instead of current flowing just one way around a circuit, it switches direction super-fast. This 'switching' happens 60 times per second in a standard household circuit. This variation in current forms a sine curve when plotted on a graph, like this one for example.

While the basic structure of an RLC circuit is simple, completing calculations isn't always so simple. An RLC circuit is an example of a **resonant circuit**, one where the capacitor and inductor fight each other to increase and decrease the resistance (or 'impedance') of the circuit. At resonance, the two cancel each other out; in which case, the total impedance of the circuit is just equal to the resistance of the resistor. To fully interpret RLC circuits you often end up using an equation with complex numbers and all kinds of involved mathematics. But in this lesson, we're just going to look at simple series RLC circuits that are at resonance. This will make things easier for us.

There are several important equations that help us understand RLC circuits. We said in another lesson that the resistance (or impedance) of a capacitor and inductor (XC and XL) are given by these two equations, where *f* is the frequency of the AC power source measured in Hertz, *C* is the capacitance of the capacitor measured in farads and *L* is the inductance of the inductor measured in Henrys. The resistance of the resistor is just *R*, like in any circuit.

For a series RLC circuit that's in resonance, XC and XL will be equal to each other and cancel each other out. Therefore, *R* becomes the total resistance of the circuit. That only happens when this third equation is true. Again, in this equation *f* is the frequency of the power source, *C* is the capacitance of the capacitor and *L* is the inductance of the inductor.

The only other equation you might need (also discussed in another lesson) is Ohm's Law, which says that the current (*I*) measured in amps is equal to the voltage (*V*) measured in volts, divided by the resistance(*R*) measured in Ohms. This can be used for individual components, like the resistor, or the capacitor or inductor, or it can be used for the totals... the total current of the circuit, total voltage and total resistance. Doing these two calculations using Ohm's Law separately can help you solve problems.

Remember that when you use Ohm's Law for a capacitor, instead of *R*, you use the symbol XC. And when you use Ohm's Law for an inductor, instead of *R*, you use the symbol XL. If this is confusing, I recommend you watch the lesson on impedance first, and then come back to this later.

Maybe this would be easier if we went through an example problem. Let's say you have a resonant RLC circuit, connected to a 12 V AC power supply. The capacitance of the capacitor is 2 * 10^-6 farads, the inductance of the inductor is 2 Henrys, and the resistance of the resistor is 5 Ohms. You're asked to calculate:

A) The frequency of the power supply, *f*

B) The current flowing in the circuit, *I*

C) The voltage across the capacitor, VC.

First of all, let's write out what we know. We know that the voltage of the power supply, *V*, is 12 V. We know that *C* = 2 * 10^-6 farads, we know that *L* is equal to 2 Henrys and we know that *R* is equal to 5 Ohms. Part A asks us to find *f*. Taking a look at our equations, we'll see that we know everything except *f* in this equation. So, that's the one to use. Plug in *L* and *C*, type it into a calculator, and we get 79.6 Hz.

Part B asks us to figure out the current flowing in the circuit. Ohm's Law is the only equation in this lesson that contains current. Since this is a series circuit, the current is the same all the way around the loop. So we could use Ohm's Law for the whole circuit, or the resistor, or the capacitor, or the inductor; either way, *I*, will come out the same. But we just don't have enough information about any of the individual components to do a calculation for them, at least not without using more than one equation.

The easiest way to solve this is to use Ohm's Law for the totals - for the whole circuit. *I* = the total voltage (VT) / the total resistance of the circuit (RT). We were told in the question that the voltage of the power supply is 12 V, so that's the total voltage. And since this RLC circuit is in resonance, the total resistance is just equal to the resistance of the resistor, which is 5 Ohms. Plug that into the equation and solve for the current, *I*, and we get 2.4 amps.

Part C asks for the voltage across the capacitor, VC. To figure that out we'll need to use Ohm's Law just for the capacitor. Rearrange Ohm's Law to find out that the voltage is equal to the current, multiplied by the resistance (or impedance) of the capacitor XC. We already know the current is 2.4 amps, and we can find out the resistance by plugging numbers into our capacitor equation. We'll plug in the frequency, 79.6 Hz we calculated in part A, and the capacitance of 2 * 10^-6 farads. Type that into a calculator, and you'll get approximately 1000 for the resistance of the capacitor. Then plug that resistance into Ohm's Law to get a voltage of 2400 volts. And that's it; we're done!

An **RLC series circuit** is a circuit where a battery, resistor (with resistance *R*), an inductor (with inductance *L*) and a capacitor (with capacitance *C*), are all connected in one complete loop (a series circuit). An RLC circuit looks something like this. They're often used as tuning circuits in analogue radios and as low-pass, high-pass or band-pass filters when recording audio in a studio.

For an RLC circuit to operate, it also has to be an **alternating current** (or AC) circuit, which is where, instead of current flowing just one way around the circuit, it switches direction super-fast. An RLC circuit is an example of a **resonant circuit**, one where the capacitor and inductor fight each other to increase and decrease the resistance (or 'impedance') of the circuit. At resonance, the two cancel each other out, in which case the total impedance of the circuit is just equal to the resistance of the resistor.

Here are the relevant equations for this topic. The resistance (or impedance) of a capacitor and inductor (XC and XL) are calculated using the frequency of the power source (*f*) measured in Hertz, the capacitance of the capacitor (*C*) measured in farads and the inductance of the inductor (*L*) measured in Henrys. For an RLC circuit that's in resonance, XC and XL will be equal to each other and cancel each other out. Therefore *R* becomes the total resistance of the circuit. Resonance only happens when this third equation is true.

To solve problems, you're also likely to need Ohm's Law, which says that the current (*I*) measured in amps, is equal to the voltage (*V*) measured in volts, divided by the resistance (*R*) measured in Ohms. This can be used for individual components, like the resistor, or capacitor or the inductor, or it can be used for the totals: the total current of the circuit, total voltage and total resistance.

After you have finished, you should be able to:

- Describe an RLC circuit and identify its components
- Recall what a resonant circuit is
- Recite the equations relevant to understanding RLC circuits and Ohm's Law

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UExcel Physics: Study Guide & Test Prep18 chapters | 201 lessons | 13 flashcard sets

- Go to Vectors

- Go to Kinematics

- Insulators and Conductors: Examples, Definitions & Qualities 6:38
- What is Electric Current? - Definition, Unit & Types 7:59
- Electrical Resistance: Definition, Unit & Variables 7:52
- Ohm's Law: Definition & Relationship Between Voltage, Current & Resistance 7:17
- What is Electric Power? 6:41
- Applying Kirchhoff's Rules: Examples & Problems 7:29
- Resistor-Capacitor (RC) Circuits: Definition & Explanation 6:28
- Impedance in Alternating Current Circuits 5:53
- R-L-C Series Circuits 8:01
- Go to Circuits in Physics

- Go to Relativity

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