AI Tutor
If you put a 40 Ω40\,\Omega resistor in series with a 30 Ω30\,\Omega resistor, the total opposition is simple: 70 Ω70\,\Omega.
Yet, if you replace the second resistor with a capacitor providing 30 Ω30\,\Omega of opposition, an AC source 'sees' only 50 Ω50\,\Omega instead of 70 Ω70\,\Omega.
Why doesn't simple addition work for reactive AC components?

The 90∘90^\circ Phase Split

A resistor's voltage peaks at the exact same instant as its current, meaning they are in phase (0∘0^\circ phase shift).
A capacitor stores charge, so its voltage lags behind the alternating current by exactly 90∘90^\circ (one quarter cycle).
A capacitor's opposition to alternating current is called capacitive reactance (XCX_C), measured in ohms (Ξ©\Omega) and calculated as XC=12Ο€fCX_C = \frac{1}{2\pi f C}.
Because resistance (RR) and capacitive reactance (XCX_C) act 90∘90^\circ apart in time, we cannot simply add them like standard numbers.
How can we combine two perpendicular electrical quantities into a single total value?

The Impedance Triangle

We represent AC values using phasorsβ€”rotating vectors where length represents magnitude and angle represents phase timing.
The combined total opposition of a circuit containing both resistance and reactance is called impedance (ZZ), also measured in ohms (Ξ©\Omega).