Content

• Formulas
• Steps
• Part 1 of 2: Calculating Active and Reactive Impedances
• Part 2 of 2: Calculating Impedance
• Tips

Impedance, or impedance, refers to the resistance of a circuit to an alternating electrical current. This value is measured in ohms. To calculate the total resistance of a circuit, it is necessary to know the values ​​of all active resistances (resistors) and the impedance of all inductors and capacitors included in this circuit, and their values ​​change depending on how the current passing through the circuit changes. Impedance can be calculated using a simple formula.

Formulas

1. Impedance Z = R or X_Lor X_C (if one thing is present)
2. Total resistance (serial connection) Z = √ (R + X) (if R and one type X are present)
3. Total resistance (serial connection) Z = √ (R + (| X_L - X_C|)) (if R, X_L, X_C)
4. Total resistance (any connection) = R + jX (j is the imaginary number √ (-1))
5. Resistance R = I / ΔV
6. Inductive resistance X_L = 2πƒL = ωL
7. Capacitive resistance X_C = / _2πƒL = / _ωL

Steps

Part 1 of 2: Calculating Active and Reactive Impedances

1. 1 Impedance is indicated by the symbol Z and is measured in ohms (ohms). You can measure the impedance of an electrical circuit or an individual element. Impedance characterizes the resistance of a circuit to an alternating electrical current. There are two types of resistance that contribute to impedance:
   • The active resistance (R) depends on the material and shape of the element. Resistors have the highest active resistance, but other elements of the circuit also have low active resistance.
   • Reactive resistance (X) depends on the magnitude of the electromagnetic field. The highest reactance is possessed by inductors and capacitors.
2. 2 Resistance is a fundamental physical quantity described by Ohm's law: ΔV = I * R. This formula will allow you to calculate any of the three quantities if you know the other two. For example, to calculate resistance, rewrite the formula as follows: R = I / ΔV. You can also measure resistance with a multimeter.
   • ΔV is the voltage (potential difference) measured in volts (V).
   • I is the current strength, measured in amperes (A).
   • R is the resistance measured in ohms (ohms).
3. 3 Reactive resistance occurs only in AC circuits. Like resistance, reactance is measured in ohms (ohms). There are two types of reactance:
   • Inductive resistance X_C have inductors that create a magnetic field that prevents the change in the direction of the current in the circuit. The faster the direction of the current changes, the greater the inductive reactance.
   • Capacitance X_C have capacitors that store an electrical charge. When the direction of the current in the circuit changes, the capacitor repeatedly zeroes and accumulates an electric charge. The longer the capacitor charges, the greater the capacitive resistance.Therefore, the faster the direction of the current changes, the lower the capacitive resistance.
4. 4 Calculate the inductive reactance. This resistance is directly proportional to the speed of the change in the direction of the current, that is, the frequency of the current. This frequency is indicated by the symbol ƒ and is measured in hertz (Hz). Formula for calculating inductive reactance: X_L = 2πƒLwhere L is the inductance measured in henry (H).
   • The inductance L depends on the number of turns in the inductor. You can also measure the inductance.
   • If you are familiar with the unit circle, then imagine that one cycle of alternating current is equal to one complete rotation of this circle (by 2π radians). If you multiply this value by ƒ, which is measured in hertz (units per second), you get the result, measured in radians per second. It is a unit of measure for angular velocity and is denoted by ω. You can rewrite the formula to calculate the inductive reactance like this: X_L= ωL
5. 5 Calculate capacitance. This resistance is inversely proportional to the speed at which the direction of the current changes, that is, the frequency of the current. Formula for calculating capacitance: X_C = / _2πƒC... C is the capacitance of a capacitor, measured in farads (F).
   • You can measure electrical capacitance.
   • This formula can be rewritten as follows: X_C = / _ωL (see explanations above).

Part 2 of 2: Calculating Impedance

1. 1 If the circuit consists solely of resistors, then the impedance is calculated as follows. First measure the resistance of each resistor or see the resistance values ​​on the circuit diagram.
   • If the resistors are connected in series, then the impedance R = R₁ + R₂ + R₃...
   • If the resistors are connected in parallel, then the impedance R = / _R1 + / _R2 + / _R3 ...
2. 2 Add up the same reactances. If the circuit contains solely inductors or exclusively capacitors, then the impedance is equal to the sum of the reactances. Calculate it like this:
   • Series connection of coils: X_total = X_L1 + X_L2 + ...
   • Series connection of capacitors: C_total = X_C1 + X_C2 + ...
   • Parallel connection of coils: X_total = 1 / (1 / X_L1 + 1 / X_L2 ...)
   • Parallel connection of capacitors: C_total = 1 / (1 / X_C1 + 1 / X_C2 ...)
3. 3 Subtract inductive and capacitive reactances to get the total reactance. Since with an increase in one type of resistance, the other decreases, they, as a rule, compensate each other. To find the total reactance, subtract the lower resistance from the larger one.
   • Or use the formula: X_total = | X_C - X_L|
4. 4 Calculate the impedance and reactance in the series circuit. You cannot just add these values, since they change over time, but reach their maximum values ​​at different times. Therefore, use the formula:Z = √ (R + X).
   • Calculations with this formula involve the use of vectors, but you can use the Pythagorean theorem by representing R and X as the legs of a right triangle, and the resistance Z as the hypotenuse.
5. 5 Calculate the impedance and reactance in the parallel circuit. In this case, complex numbers are used (this is the only way to calculate the impedance in a parallel circuit that has both resistance and reactance).
   • Z = R + jX, where j is the imaginary unit: √ (-1). Use j instead of i to avoid confusing imaginary unit (j) with amperage (I).
   • You cannot add these numbers. For example, impedance can be represented as 60 ohms + j120 ohms.
   • If you have two consecutive chains, then you can add natural numbers separately and complex ones separately. For example, if Z₁ = 60 Ohm + j120 Ohm, and a resistor with Z is connected in series to this circuit₂ = 20Ω, then Z_total = 80Ω + j120Ω.

Tips

• Total resistance (resistance and reactance) can also be expressed through an imaginary number.