How to Calculate Impedance: 10 Steps (with Pictures)

2024 Author: Samantha Chapman | [email protected]. Last modified: 2024-01-15 13:47

Impedance represents the force of opposition of a circuit to the passage of alternating electricity, and is measured in ohms. To calculate it, you need to know the value of all the resistors and the impedance of all the inductors and capacitors that oppose a variable resistance to the current flow based on how this changes. You can calculate the impedance thanks to a simple mathematical formula.

Summary of the Formula

1. The impedance Z = R, or Z = L, or Z = C (if there is only one component).
2. Impedance for i only circuits in series Z = √ (R² + X²) (if R and a type of X are present).
3. Impedance for i only circuits in series Z = √ (R² + (| X_L - X_C.|)²) (if R, X_L and X_C. are all present).
4. Impedance in any type of circuit = R + jX (j is the imaginary number √ (-1)).
5. Resistance R = I / ΔV.
6. Inductive reactor X_L = 2πƒL = ωL.

7. Capacitive reactor X_C. = ¹ / _2πƒC = ¹ / _ωC.

   Steps

   Part 1 of 2: Calculate Resistance and Reactance

   

   Step 1. Define the impedance

   The impedance is represented by the letter Z and is measured in ohms (Ω). You can measure the impedance of each electrical circuit or component. The result tells you how much the circuit is opposed to the passage of electrons (i.e. current). There are two different effects that slow down the flow of current and both contribute to the impedance:

   • The resistance (R) is determined by the shape and material of the components. This effect is most noticeable with resistors, but all elements of a circuit have some resistance.
   • Reactance (X) is determined by magnetic and electric fields that oppose changes in current or voltage. It is most noticeable in capacitors and inductors.

   

   Step 2. Review the concept of resistance

   This is a fundamental part of the study of electricity. You will often encounter it in Ohm's Law: ΔV = I * R. This equation allows you to calculate any of the three values knowing the other two. For example, to calculate the resistance, you can reformulate the equation according to the terms R = I / ΔV. You can also measure resistance with a multimeter.

   • ΔV represents the current voltage, measured in volts (V). It is also called potential difference.
   • I is the current intensity and is measured in amperes (A).
   • R is resistance and is measured in ohms (Ω).

   

   Step 3. Know what kind of reactance you need to calculate

   This is present only in alternating current circuits. Just like resistance, it is measured in ohms (Ω). There are two types of reactance found in different electrical components:

   • The inductive reactance X_L it is generated by inductors, also called coils. These components create a magnetic field that opposes the directional changes of the alternating current. The faster the directional changes, the higher the inductive reactance.
   • The capacitive reactance X_C. it is produced by capacitors which hold an electrical charge. When alternating current flows through a circuit and changes direction, the capacitor charges and discharges repeatedly. The more the capacitor has to charge, the more it opposes the flow of current. For this reason, the faster the directional changes are, the lower the capacitive reactance.

   

   Step 4. Calculate the inductive reactance

   As described above, this increases with increasing speed of direction changes, or frequency of the circuit. The frequency is represented by the symbol ƒ and is measured in hertz (Hz). The complete formula for calculating inductive reactance is: X_L = 2πƒL, where L is the inductance measured in henry (H).

   • The inductance L depends on the characteristics of the inductor, such as the number of its turns. It is also possible to measure inductance directly.
   • If you are able to think in terms of a unit circle, imagine the alternating current as a circle whose full rotation is equal to 2π radians. If you multiply this value by the frequency ƒ measured in hertz (units per second) you get the result in radians per second. This is the angular velocity of the circuit and is denoted by the lowercase letter omega ω. You can also find the formula of inductive reactance expressed as X_L= ωL.

   

   Step 5. Calculate the capacitive reactance

   Its formula is quite similar to that of inductive reactance, except that capacitive reactance is inversely proportional to frequency. The formula is: X_C. = ¹ / _2πƒC. C is the electrical capacitance or capacitance of the capacitor measured in farads (F).

   • You can measure the electrical capacity with a multimeter and some simple calculations.
   • As explained above, it can be expressed as ¹ / _ωL.

   Part 2 of 2: Calculate the Total Impedance

   

   Step 1. Add all the resistors of the same circuit together

   Calculating the total impedance is not difficult if the circuit has several resistors but no inductor or capacitor. First measure the resistance of each resistor (or component that opposes a resistance), or refer to the circuit diagram for these values indicated in ohms (Ω). Proceed to the calculation considering the way in which the elements are connected:

   • If the resistors are in series (connected along a single wire in a head-to-tail order), then you can add the resistors together. In this case the total resistance of the circuit is R = R.₁ + R₂ + R₃…
   • If the resistors are in parallel (each is connected with its own wire to the same circuit) then the reciprocals of the resistances must be added. The total resistance is equal to R = ¹ / _{R.1 + ¹ / R.2 + ¹ / R.3 …}

   

   Step 2. Add the similar circuit reactors

   If there are only inductors or only capacitors, the impedance is equal to the total reactance. To calculate it:

   • If the inductors are in series: X_total = X_L1 + X_L2 + …
   • If the capacitors are in series: C_total = X_C1 + X_C2 + …
   • If the inductors are in parallel: X_total = 1 / (1 / X_L1 + 1 / X_L2 …)
   • If the capacitors are in parallel: C._total = 1 / (1 / X_C1 + 1 / X_C2 …)

   

   Step 3. Subtract the inductive and capacitive reactance to get the total reactance

   Since these are inversely proportional, they tend to cancel each other out. To find the total reactance, subtract the smaller value from the larger one.

   You will get the same result from the formula: X_total = | X_C. - X_L|.

   

   Step 4. Calculate the impedance from the resistance and reactance connected in series

   In this case, you cannot simply add, as the two values are "out of phase". This means that both values change with time according to the cycle of the alternating current, however, reaching each other's peaks at different times. Thankfully, if all the elements are in series (connected by the same wire), you can use the simple formula Z = √ (R² + X²).

   The mathematical concept underlying the equation involves the use of "phasors", but you can also deduce it geometrically. You can represent the two components R and X as the legs of a right triangle and the impedance Z as the hypotenuse

   

   Step 5. Calculate the impedance with the resistance and reactance in parallel

   This is the general formula for expressing the impedance, but it requires the knowledge of complex numbers. This is also the only way to calculate the total impedance of a parallel circuit that includes both resistance and reactance.

   • Z = R + jX, where j is the imaginary number: √ (-1). We use j instead of i to avoid confusion with the intensity of the current (I).
   • You cannot combine the two numbers together. For example an impedance must be expressed as 60Ω + j120Ω.
   • If you have two circuits like this but in series, you can add the imaginary component with the real one separately. For example, if Z₁ = 60Ω + j120Ω and is in series with a resistor with Z₂ = 20Ω, then Z_total = 80Ω + j120Ω.