Formula for impedance in electronics (RL RLC & LC circuit)

We know that the opposition to the current flow through a conductor is called resistance. Impedance is almost the same as resistance, but with a slightly different concept. In this article, we are going to discuss the definition, units and formula for impedance in different electronic circuits. The impedances of a pure resistor, pure capacitor, pure inductor, series LC, RC and RLC circuits will also be discussed here.

Table of Contents

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‘. Impedance is the general term for the opposition. The resistance is a special case of impedance. This is the relation between impedance and resistance.

Units of impedance

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

The impedance of a pure resistor

The impedance for a pure resistor is its resistance. Different combinations of resistors will offer different resistances.

Formula for impedance of a pure capacitor

Let the capacitance of a capacitor is C and the alternating current passing through the capacitor circuit have 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 is the inductance of an inductor operating by an 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.

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)

Both real and imaginary parts of the impedance exist in the impedance formula of an AC circuit with series R and L. The term $\small {\color{Blue}\omega L}$ gives the impedance of an inductor.

Formula for impedance of RC circuit

A series CR circuit will offer the opposition to the current flow due to both the 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 a 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 be 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 a 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. Also, we have explored the formula for impedance of AC circuits like RL, LC, RLC, RC and pure resistor, capacitor and inductor. We became to know that resistance is a special type of impedance. Resistance does not include the imaginary term in its expression.

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

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