[Physics Class Notes] on Reactance and Impedance Pdf for Exam

Impedance meaning – It is the measure of overall opposition of an AC circuit to current denoted by Z. In simple words, it gives the amount of circuit that impedes the flow of change. Impedance is like resistance, which also takes into account the effects of inductance and capacitance. The measurement unit for Impedance is ohms.

As impedance considers the effects of inductance and capacitance and varies with the frequency of current passing through the circuit, it is more complex than resistance. As compared to resistance, which is constant regardless of frequency, the impedance varies with frequency.

When it comes to defining reactance, it is the measure of the opposition of inductance and capacitance to current. Let’s learn more about these two terms in brief.

Impedance Formula

The mathematical symbol of impedance is Z, and the unit of measurement is the ohm. It is the superset of both resistance and reactance combined.

In phasor terms, impedance Z is characterized as a summation of resistance R and reactance X as:

X = R + j X

Where reactance X is the summation of iInductive reactance X[_{L}] and capacitive X[_{C}].

X = X[_{L}] – X[_{C}]

Impedance, Z = [frac{V}{I}]

V = voltage in volts (V)

I = current in amps (A)

Z= impedance in ohms (Ω)

R= resistance in ohms (Ω)

Impedance can be split into two parts:

The alternating current lags or leads the voltage depending upon the nature of the reactance component of impedance (whether predominantly inductive or capacitance).

The inductance and capacitance cause phase shifts between current and voltage, which means the resistance and reactance cannot be simply summed up to give impedance. Instead, they must be summed up as vectors with reactance at right angles to resistance, as shown in the figure below.

Impedance Z  = [sqrt{R^{2}+X^{2}}]

There are four electrical quantities that determine the impedance (Z) of a circuit: These are resistance (R), capacitance (C), inductance (L), and frequency (f).

What is Reactance?

The measure of the opposition of inductance and capacitance to current in an AC circuit is known as reactance, denoted by X. It varies with the frequency of electrical signals and is measured in ohms.

Reactance is of two types:

• Capacitive reactance ( X[_{C}] ), and

• Inductive reactance ( X[_{L}] ).

Reactance Formula

The total reactance (X) is equal to the difference between the two:

Total reactance, X = X[_{L}]– X[_{C}]

a. Capacitive Reactance X[_{C}]

The reactance, which is large at low frequencies and small at high frequencies is known as capacitive reactance ( X[_{C}] ). X[_{C}] is infinite for steady DC, at zero frequency (f=0Hz). This means that the capacitor passes AC but blocks DC.

Capacitive Reactance, X[_{C}] = 1/2fC

Where,

X[_{C}] = reactance in ohms (Ω)

f = frequency in hertz (Hz)

C = capacitance in farads (F)

For example, 1µF capacitor has a reactance of 3.2k for a 50Hz signal, but when a frequency is higher at 10kHz, the reactance is only 16.

b. Inductive Reactance, X[_{L}]

The reactance which is small at low frequencies and large at high frequencies is known as inductive reactance. X[_{L}] is zero for steady DC, at zero frequency (f=0Hz). This means that the inductor passes DC but blocks AC.

The formula for calculating the inductive reactance of a coil is:

Inductive reactance, or X[_{L}] is a product of 2 times (pi), or 6.28, frequency of the ac current in hertz, and the inductance of the coil, in henries.

X[_{L}] = 2x f x L

L = the inductance value of coil in henries.

Inductive reactance, X[_{L}] = 2fL

Where,

X[_{L}] = reactance in ohms (Ω)

f    = frequency in hertz (Hz)

L   =inductance in henry (H)

For example, a 1mH inductor has a reactance of only 0.3 for a 50Hz signal, but when the frequency is higher at 10 kHz, its reactance is 63 .

Reactance and Impedance Formula

An element in the DC circuit can be easily described by using only its resistance. The resistance of a capacitor in DC circuits is regarded to be an open connection whereas the resistance of an inductor in a DC circuit will be regarded as a short connection or zero resistance. As opposed to DC circuits, it is seen that in AC circuits, the impedance of an element is a value of how much the element tends to oppose the flow of current when an AC voltage is being applied across it. Impedance can be represented as  a complex number that consists of both real and imaginary parts and can be represented as follows:

Z = R + jX

Where Z represents the impedance

R represents the value of resistance

X which is the imaginary part will represent reactance

It is seen that the resistance seen in the circuit will always be positive while the reactance that is seen will be either positive or negative.

Do you know?

When current and voltage are out of step with each other, it means there is a phase shift. For example, when you charge a capacitor, the voltage across it is zero. However, the current is maximum. When the capacitor is charged, the voltage will be maximum, and the current will be at a minimum. The charging and discharging occur continually with AC, where the current reaches maximum shortly before the voltage reaches the maximum, so it is called current leading voltage.