AC Circuit Resistance: Calculate Impedance and Reactance

Calculate resistance in an AC circuit by separating true resistance from reactance, then combining them as impedance. Enter resistance and either inductive reactance, capacitive reactance, or both; the calculator returns the circuit’s impedance magnitude in ohms, with the signed net reactance shown as a helper.

Formula

For a series AC circuit containing resistance and ideal inductive and capacitive reactance, the impedance magnitude is:

Z = √[R² + (X_L − X_C)²]

• Z is impedance magnitude, measured in ohms (Ω).
• R is resistance, measured in ohms (Ω).
• X_L is inductive reactance, measured in ohms (Ω).
• X_C is capacitive reactance, measured in ohms (Ω).
• X = X_L − X_C is net reactance, in ohms (Ω); positive values indicate net inductive behavior, and negative values indicate net capacitive behavior.

The calculator assumes the entered values are for a series circuit at one frequency. It reports impedance magnitude, not resistance alone. In an AC circuit, resistance is the part of opposition that dissipates energy as heat; reactance is the part associated with energy storage and return in inductors and capacitors.

Worked Example

Using the calculator’s defaults, R = 100 Ω, X_L = 50 Ω, and X_C = 50 Ω:

1. Find net reactance: X = 50 − 50 = 0 Ω.
2. Substitute into the impedance formula: Z = √[100² + 0²].
3. Evaluate: Z = √10,000 = 100 Ω.

The result is an impedance magnitude of 100.00 Ω, with net reactance of 0.00 Ω. The inductive and capacitive effects cancel at these values, so the circuit’s impedance is purely resistive in this idealized model.

Resistance, Reactance, and Impedance

In a direct-current circuit after steady conditions are established, an ideal resistor’s opposition is described by resistance. AC continually changes direction, and voltage and current may not reach their peaks together. Inductors and capacitors cause this phase difference, so their opposition cannot generally be combined with resistance by ordinary addition.

Impedance, written Z, is the overall opposition to AC. In a series circuit it is a complex quantity: its real part is resistance and its imaginary part is net reactance. The formula above calculates its magnitude, √(R² + X²). A magnitude in ohms alone does not say whether the circuit is inductive or capacitive; the sign of X, or a phase angle, supplies that information.

For a purely resistive circuit, X = 0 and Z = R. For a circuit with no resistance but nonzero reactance, Z = |X|. If inductive and capacitive reactances are equal in a series circuit, they cancel in the net reactance calculation; the remaining impedance is R.

Finding Reactance from Frequency

Reactance depends on frequency as well as component value. For an ideal inductor and capacitor, use:

• X_L = 2πfL, where f is frequency in hertz (Hz), L is inductance in henries (H), and X_L is in ohms.
• X_C = 1 ÷ (2πfC), where C is capacitance in farads (F), f is in hertz, and X_C is in ohms.

As frequency rises, an ideal inductor’s reactance rises, while an ideal capacitor’s reactance falls. For example, a 0.1 H inductor at 60 Hz has X_L ≈ 37.70 Ω: 2π × 60 × 0.1. A 100 μF capacitor at 60 Hz has X_C ≈ 26.53 Ω, after converting 100 μF to 0.0001 F. These values can then be used in the series impedance formula with the resistor value.

Using Impedance to Find Current

Once impedance magnitude is known, the magnitude of current in a sinusoidal AC circuit can be found from Ohm’s law: I = V ÷ Z. Here V is RMS voltage in volts, Z is impedance magnitude in ohms, and I is RMS current in amperes. For example, 120 V RMS across a 100 Ω impedance gives 1.2 A RMS, provided the circuit is described by the assumed series model.

Use RMS voltage and current for ordinary AC power calculations unless a problem explicitly specifies peak values. For a sinusoidal waveform, RMS voltage is the peak voltage divided by √2. Mixing peak voltage with an RMS impedance-based calculation produces a misleading current result.

Series and Parallel Circuits

The calculator is specifically for a series circuit: the same current passes through each component, and the resistance and reactance combine into one total impedance. For parallel branches, do not apply the series formula directly to the component values. Instead, combine complex impedances using reciprocal relationships, or work with admittance; the branch voltage is shared, while current divides among branches.

Real components can also have additional effects. A coil has winding resistance, and a capacitor may have losses; these should be included in a suitable circuit model when accuracy matters. At high frequencies, wiring, component parasitics, and changing component behavior may make a simple ideal RLC calculation inadequate.

Common Mistakes and Limits

• Calling impedance resistance: Z includes the effect of reactance. Resistance alone is R.
• Adding reactances without signs: In a series circuit, inductive and capacitive reactance oppose one another, so use X_L − X_C.
• Using inconsistent units: Convert frequency to hertz, inductance to henries, and capacitance to farads before calculating reactance. The final impedance is in ohms.
• Applying the formula to a parallel circuit: The equation here assumes a series arrangement.
• Ignoring frequency: Reactance changes with frequency, so a circuit does not necessarily have one fixed impedance for all AC signals.

For a measured circuit, use values appropriate to the signal frequency and account for component tolerances and measurement conditions. The calculation does not determine component power ratings, voltage safety, or the full behavior of nonlinear or frequency-dependent devices.

Frequently Asked Questions

Is resistance the same as impedance in an AC circuit?
No. Resistance is the dissipative part of opposition, while impedance includes resistance and reactance. They are equal in magnitude only for a purely resistive circuit or when net reactance is zero.

How do I calculate AC resistance from voltage and current?
If voltage and current are in phase in a purely resistive circuit, R = V_RMS ÷ I_RMS. If they are out of phase, that ratio gives impedance magnitude rather than resistance alone; phase information or a circuit model is needed to separate the two.

Why do inductive and capacitive reactance subtract?
They produce opposite signs of phase shift. In a series circuit their signed effects combine as X_L − X_C; the remaining reactance can be inductive, capacitive, or zero.

What happens when X_L equals X_C?
In an ideal series circuit, net reactance is zero and impedance magnitude equals resistance. This condition is called series resonance; real components still have losses and may not behave ideally.

Can I use this calculation for a parallel AC circuit?
Not directly. This calculator’s formula is for series components. For parallel circuits, combine branch impedances using complex arithmetic or admittance, taking account of each branch’s resistance and reactance.

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in r | Resistance | ohm | 100 | 0
in xl | Inductive reactance | ohm | 50 | 0
in xc | Capacitive reactance | ohm | 50 | 0
out z | Impedance magnitude | ohm | sqrt(r^2 + (xl - xc)^2) | 2
out x | Net reactance | ohm | xl - xc | 2