Impedance is a measure of resistance to alternating current. The unit is ohms. To calculate impedance, you need to know the sum of all resistances as well as the impedances of all inductors and capacitors which will give a varying amount of resistance to current depending on changes in current. You can calculate impedance using a simple mathematical formula.
- Impedance Z = R or XL or XC (if only one is known)
- Impedance in series Z = (R2 + X2) (if R and one of X are known)
- Impedance in series Z = (R2 + (|XL - XC|)2) (if R, XL, and XC fully known)
- Impedance in all kinds of networks = R + jX (j is an imaginary number (-1))
- Resistance R = I / V
- Inductive reactance XL = 2πƒL = L
- Capacitive reactance XC = 1 / 2πƒL = 1 / L
Part 1 of 2: Calculating Resistance and Reactance
Step 1. Definition of impedance
Impedance is denoted by the symbol Z and has units of Ohms (Ω). You can measure the impedance of any circuit or electrical component. The measurement results will tell you how much the circuit is blocking the flow of electrons (current). There are two distinct effects that slow the rate of current, both contributing to impedance:
- Resistance (R) or resistance is the slowing of the current caused by the material and shape of the component. This effect is greatest in resistors, although all components must have at least some resistance.
- Reactance (X) is the slowing down of current due to electric and magnetic fields that resist changes in current or voltage. This effect is most significant for capacitors and inductors.
Step 2. Review resistance
Resistance is a basic concept in the field of electrical studies. You can see this in Ohm's law: V = I * R. This equation allows you to calculate the values of these variables as long as you know at least two of the three variables. For example, to calculate resistance, write the formula as R = I / V. You can also easily calculate resistance with a multimeter.
- V is the voltage, the unit is Volts (V). This variable is also referred to as the potential difference.
- I is the current, the unit is Ampere (A).
- R is resistance, the unit is Ohms (Ω).
Step 3. Figure out the type of reactance to calculate
Reactance only occurs in alternating current (AC) circuits. Similar to resistance, reactance has units of Ohms (Ω). There are two types of reactance present in different electrical components:
- Inductive reactance XL produced by the inductor, also known as the coil or reactor. These components produce a magnetic field that resists changes in direction in an alternating current circuit. The faster the change in direction occurs, the greater the value of the inductive reactance.
- Capacitive reactance XC generated by a capacitor that stores an electric charge. As the current flow in an AC circuit changes direction, the capacitor will charge and discharge repeatedly. The longer the capacitor has to charge, the more the capacitor will resist current. Therefore, the faster the direction change occurs, the lower the resulting capacitive reactance value.
Step 4. Calculate the inductive reactance
As described above, the inductive reactance will increase with the rate of change in the direction of the current, or frequency of the circuit. This frequency is denoted by the symbol, and has units of Hertz (Hz). The complete formula for calculating inductive reactance is XL = 2πƒL, where L is the inductance with units of Henry (H).
- The inductance L depends on the characteristics of the inductor used, such as the number of coils. You can also measure inductance directly.
- If you recognize the unit circle, imagine an alternating current represented by a circle, and one complete rotation of 2π radians representing one cycle. When you multiply this by which is in Hertz (units per second), you get the result in radians per second. This is the angular velocity of the circuit and can be written in lower case as omega. You can write the formula for inductive reactance in XL=ωL
Step 5. Calculate the capacitive reactance
This formula is similar to the formula for finding inductive reactance, but capacitive reactance is inversely proportional to frequency. Capacitive reactance XC = 1 / 2πƒC. C is the capacitance value of the capacitor, in Farads (F).
- You can measure capacitance using a multimeter and some basic calculations.
- As explained above, this variable can be written in 1 / L.
Part 2 of 2: Calculating Total Impedance
Step 1. Add up the resistances in the same circuit
The total impedance is easy to calculate when a circuit has several resistors without inductors or capacitors. First, measure the resistance value of each resistor (or any component that has resistance), or look on the circuit diagram for the parts labeled with resistance ohms (Ω). Add up according to the type of circuit between the components:
- Resistors connected in a series circuit (the ends of which are connected in a single wire line) can be summed together. The total resistance becomes R = R1 + R2 + R3…
- Resistors connected in parallel (each resistor has a different wire but connected in the same circuit) are added in reverse. The total amount of resistance becomes R = 1 / R1 + 1 / R2 + 1 / R3 …
Step 2. Add up the reactance values in the same circuit
When there are only inductors in a circuit, or only capacitors, the total impedance is equal to the total reactance. Calculate as follows:
- Inductor in series: Xtotal = XL1 + XL2 + …
- Capacitors in series: Ctotal = XC1 + XC2 + …
- Inductor in parallel circuit: Xtotal = 1 / (1/XL1 + 1/XL2 …)
- Capacitor in parallel circuit: Ctotal = 1 / (1/XC1 + 1/XC2 …)
Step 3. Subtract the inductive reactance by the capacitive reactance to get the total reactance
Since the effect of one reactance increases as the effect of the other reactance decreases, the two reactances tend to reduce each other's effect. To find the total value, subtract the larger reactance value by the smaller reactance value.
- You will get the same result from the formula Xtotal = |XC - XL|
Step 4. Calculate the impedance of the resistance and reactance in a series circuit
You can't add them together because the two values are in different phases. That is, their values change over time as part of the AC cycle, but they peak at different times. Fortunately, when all the components are in series (there is only one wire), we can use the simple formula Z = (R2 + X2).
The calculations behind this formula involve "phasors," although they also seem to be related to geometry. We can represent the two components R and X as the two sides of a right triangle, with the impedance Z as the perpendicular side
Step 5. Calculate the impedance of the resistance and reactance in a parallel circuit
This is a common way of calculating impedance, but requires an understanding of complex numbers. This is the only way to calculate the total impedance of a parallel circuit involving resistance and reactance.
- Z = R + jX, with j as the imaginary component: (-1). Use j instead of i to avoid confusion with I representing current.
- You cannot combine these two numbers. For example, an impedance can be written as 60Ω + j120Ω.
- If you have two such circuits in a series, you can add the components of real numbers and imaginary components separately. For example, if Z1 = 60Ω + j120Ω and connected in series with a resistor having Z2 = 20Ω, then Ztotal = 80Ω + j120Ω.