# How to Calculate the Impedance in a Circuit

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Impedance represents the total opposition to current flow in a circuit. Many people mistakenly equate impedance with resistance. Impedance is the same as resistance in circuits that have no frequency-dependent components. However, in circuits with frequency-dependent components, such as capacitors and inductors, impedance is the sum of the resistance plus the effect of the frequency-dependent components. Frequency-dependent components are referred to as reactive components. The term reactive is used to denote the fact that the components react to frequency in a way that changes the overall impedance as a function of frequency.

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• Calculate the total resistance of the circuit. If the circuit has only one resistor, the resistance is the value of that resistor. If you have multiple resistors, use the following as a guide.

For multiple resistors connected in series: Rt = R1 + R2 + R3 ... Rn

For multiple resistors connected in parallel: Rt =1/[1/R1 + 1/R2 + 1/R3 ...1/Rn]

In both cases, the final value will be the total circuit resistance or "Rt."

• Calculate the total capacitance of the circuit. If the circuit has only one capacitor, the capacitance is the value of that capacitor. If you have multiple capacitors, use the following as a guide.

For multiple capacitors connected in series: Ct =1/[1/C1 + 1/C2 + 1/C3 ...1/Cn]

For multiple capacitors connected in parallel: Ct = C1 + C2 + C3 ... Cn

In both cases, the final value will be the total capacitance or "Ct."

• Calculate the total inductance of a circuit. If the circuit has only one inductor, the inductance of the circuit is the value of that inductor. If you have multiple inductors, use the following as a guide.

For multiple inductors connected in series: Lt = L1 + L2 + L3 ... Ln

For multiple inductors connected in parallel: Lt =1/[1/L1 + 1/L2 + 1/L3 ....1/Ln]

In both cases, the final value will be the total circuit inductance or "Lt."

• Calculate the reactance of the reactive components. Ct and Lt are the reactive components. You calculate the reactance for both components using the following formula:

Xl = (2)(pi)(f)(Lt) where Xl symbolizes the reactance of the inductor, f is the frequency, pi is 3.1415 and Lt is the total inductance you calculated in Step 3.

Xc = (2)(pi)(f)(Ct) where Xc symbolizes the reactance of the capacitor, f is the frequency, pi is 3.1415 and Ct is the total capacitance you calculated in Step 2.

As an example, let's assume the frequency, f, is 15 MHZ, Ct is 3 microfarads and Lt is 6 microhenries:

Xl = (2)(pi)(f)(Lt) = 2(3.1415)(15 x 10^6)(6 x 10^-6) = 565.47ohms

Xc = (2)(pi)(f)(Ct) = 2(3.1415)(15 x 10^6)(3 x 10^-6) = 282.7ohms

• Calculate the total reactance using the formula: Xt = Xl-Xc. Continuing with our example, Xt = 565.47ohms - 282.7ohms = 282.77ohms

• Calculate the impedance using the formula: Z = sqrt (Rt^2 + Xt^2). If we assume Rt is 300 ohms and continue with our example:

Z = sqrt [300^2 + 282.77^2] = sqrt[90,000 + 79,958] = sqrt[169,958] = 412.26 ohms

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