# Reactance

The term reactance is given to the effective resistance of a component to a.c. It is given the symbol X and is defined as:

X = amplitude of the voltage across a component/amplitude of the current flowing through it

(a) For a capacitor, i = wCV giving

Reactance of a capacitor = XC = V/wCV = 1/wC = 1/2pfC

The reactance of a capacitor is therefore inversely proportional to the frequency of the applied p.d. (since w = 2pf).

(b) For an inductor, V = wLi giving

Reactance of a inductor = XL = VwL/V = wL = 2pfL

The reactance of an inductor is therefore directly proportional to the frequency of the applied p.d.
The variation of the resistance of a resistor and the reactance of an inductor and a capacitor with the applied voltage frequency (f) is shown in Figure 1.

Example problem
Calculate the reactance of the following components at frequencies of 50 Hz and 200 kHz (long wave radio): (a) a resistor of 1000 W,
(b) a capacitor of 1000 microfarads, and
(c) a solenoid of length 10 cm, diameter 1 cm, with 5000 turns (relative permeability of core 2000).

(a) The resistance of the resistor for a.c. or d.c. is constant and equal to 1000 W.
(b) For the capacitor,
(i) at 50Hz, reactance = 1/2p fC = 1/2p x 50 x 1000 x 10-6 = 3.18 W
(ii) at 200 kHz reactance = 8x10-4 = 0.0008 W
(c) For the inductor, inductance = moAN/L = 4p x 10-7 x 2000 x 7.85 x 10-5 x 5000/0.1 = 9.86 x 10-3 H
(i) at 50 Hz, reactance = 2p fL = 2p x 50 x 9.86 x 10-3 = 3.1 W .
(ii) at 200 kHz, reactance = 12390 W = 12.39 kW .