Physics · Alternating Current · NEET
No. All three (R, X, Z) share the same SI unit, the ohm, but they mean different things. Resistance R is opposition that also converts energy to heat. Reactance X is opposition from an inductor or capacitor that only stores and returns energy (no heat). Impedance Z is the total opposition of the full AC circuit. In a pure DC or pure resistor circuit, Z = R. But the moment an inductor or capacitor is present, Z becomes larger than R because reactance adds in.
Because the voltage across R is in phase with the current, but the voltage across the reactance is 90 degrees out of phase (leads for L, lags for C). Two quantities at 90 degrees cannot be added directly; they add like the two perpendicular sides of a right triangle. So Z = sqrt(R^2 + (XL - XC)^2). Adding them straight (R + XL + XC) is the single most common NEET mistake.
Resistance depends only on the material and shape of the wire, so it stays fixed. Reactance depends on frequency: XL = 2*pi*f*L rises with frequency, and XC = 1/(2*pi*f*C) falls with frequency. This is why a capacitor blocks low frequency (DC) but passes high frequency, and an inductor does the opposite.
In a resistor the current and voltage are in phase, so power = VI is always positive and energy leaves as heat. In a pure inductor or capacitor the current is 90 degrees out of phase with voltage, so power is positive for half the cycle and negative for the other half. The average over a full cycle is zero, so reactance stores energy and gives it back, wasting none. Only the R part of impedance dissipates power.
XL = 2*pi*f*L is inductive reactance and XC = 1/(2*pi*f*C) is capacitive reactance. In a series LCR circuit their voltages point in opposite directions in the phasor diagram, so they partly cancel. The net (effective) reactance is X = XL - XC. This net X is what goes into impedance: Z = sqrt(R^2 + (XL - XC)^2).
The net impedance of a series circuit (as shown) is to be found. Given R = 10 ohm, inductive reactance X_L = 5 ohm and capacitive reactance X_C = 10 ohm.
To an ac supply of 220 V at 50 Hz, a resistor of 20 ohm, a capacitor of reactance 25 ohm and an inductor of reactance 45 ohm are connected in series. The current in the circuit and the phase angle between current and voltage are, respectively:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Z = sqrt(R^2 + (XL - XC)^2), where XL = 2*pi*f*L and XC = 1/(2*pi*f*C). Here XL - XC is the net reactance of the series LCR circuit.
All three, resistance, reactance and impedance, are measured in ohm (symbol: capital omega). Sharing a unit does not make them the same quantity.
When the reactive part is zero, that is when XL = XC (resonance) or when there is no L and C (pure resistor). Then Z = R, the current is maximum, and the phase angle is zero.
No. Resistance depends on the conductor's material, length and area, so it stays fixed. Only reactance changes with frequency: XL rises and XC falls as frequency increases.
Only the resistance R. Average power P = V*I*cos(phi) and cos(phi) = R/Z, so power depends on R. A pure reactance (inductor or capacitor) has average power zero and is called wattless.
