# Formula for impedance in electronics RL RLC & LC circuit

Impedance is a frequently used word in electronics and physics. We already have discussed the resistance of a conductor in another article. Impedance is almost the same as the resistance. But there are some differences in presentation of impedance. In this article, we are going to discuss the definition, units and formula for impedance in electronics. The impedances of a pure resistor, pure capacitor, pure inductor, series LC, RC and RLC circuits will also be discussed here.

1. Definition of impedance in electronics
2. Unit of Impedance
3. Impedance of pure resistor, capacitor and inductor
4. Impedance of series LC, RC and RLC circuit

## What is electrical impedance in electronics?

Electrical impedance is an electrical property that describes how much current flows through a conductor when a voltage is applied across its terminals. Impedance is actually the opposition to the current flow. It is denoted as the letter ‘Z‘.

You may say that the definition of impedance is similar to that of resistance. Yes, the resistance is a type of impedance. Impedance is the general term of opposition and resistance is a special case of impedance. This is the relation between impedance and resistance.

## Units of impedance

The unit of impedance is same as that of resistance. The CGS and SI unit of impedance is Ohm.

## Impedance of a pure resistor

The impedance for a pure resistor is its resistance. Click here to know about resistance and its combination.

## Formula for impedance of a pure capacitor

Let the capacitance of a capacitor is C and the alternating current passing through the capacitor circuit has the angular frequency $\small \omega$. Then the impedance experiences by the current passing through the capacitor is, $\small {\color{Blue} Z=\frac{1}{j\omega C}}$. Here, the $\small j=\sqrt{-1}$ is the imaginary unit. This is the impedance formula for capacitor.

## Formula for impedance of a pure inductor

If L be the inductance of a inductor operating by a alternating voltage of angular frequency $\small \omega$, then the impedance offered by the pure inductor to the alternating current is, $\small {\color{Blue} Z= j\omega L}$. Here, $\small j=\sqrt{-1}$ is the imaginary unit.

Read more: Impedance of an inductor

## Impedance formula for RL circuit

Let, an alternating voltage of angular frequency $\small \omega$ is applied across the series RL circuit. Then the formula of the impedance of RL circuit is, $\small {\color{Blue} Z=R+j\omega L}$……….(1)

Bothe real and imaginary part of the impedance are exist here.

## Formula for impedance of RC circuit

A series CR circuit will offer the opposition to the current flow due to both resistor and capacitor. Let, the alternating voltage of angular frequency $\small \omega$ is applied across the series RC combination. Then the formula of the impedance of RC circuit is, $\small {\color{Blue} Z=R+\frac{1}{j\omega C}}$.

or, $\small {\color{Blue} Z=R-\frac{j}{\omega C}}$………(2)

Thus the impedance in series RC circuit contains both real and imaginary parts.

## Formula for impedance of LC circuit

Let an inductor of inductance L and a capacitor of capacitance C are in series in an electrical circuit. Here, the opposition to the electric current will be due to the inductor and the capacitor collectively. If $\small \omega$ be the angular frequency of the applied alternating voltage, then the formula of the impedance offered by the series LC circuit is, $\small {\color{Blue} Z=j\omega L + \frac{1}{j\omega C}}$

or, $\small {\color{Blue} Z=j\omega L - \frac{j}{\omega C}}$

or, $\small {\color{Blue} Z=j(\omega L - \frac{1}{\omega C}})$……….(3)

Thus, the impedance in series LC circuit is purely imaginary.

## Formula for impedance of RLC circuit

If a pure resistor, inductor and capacitor be connected in series, then the circuit is called a series LCR or RLC circuit. In this circuit, the resistor, capacitor and inductor will oppose the current flow collectively. If $\small \omega$ be the angular frequency of the applied alternating voltage, then the formula for impedance of RLC circuit is, $\small {\color{Blue} Z= R+ j\omega L + \frac{1}{j\omega C}}$

or, $\small {\color{Blue} Z= R+ j\omega L - \frac{j}{\omega C}}$

or, $\small {\color{Blue} Z= R+ j(\omega L - \frac{1}{\omega C})}$…………(4)

## Discussions

In this article, we have discussed the definition and units of impedance in electronics and physics. Also, we have expressed the formula for impedance of electronics circuits like RL, LC, RLC, RC and pure resistor, capacitor and inductor. We became to know that the resistance is a special type of impedance. Resistance do not include the imaginary term in its expression.

This is all from this article on the formula of impedance in electronics circuit. If you have any doubt on this topic you can ask me in the comment section.

Thank you!

Related posts:

1. Impedance of an inductor – Inductive reactance
2. Resistance and its combinations.
3. Kirchhoff’s law (KCL and KVL)