# reactance (*X*)

A direct current connected across a resistance rises immediately when the switch is closed. But the current through an inductance rises slowly. Whenever the current in a coil of wire changes, a current is generated in the opposite direction, if it has a complete circuit to flow around.

The A-4b, a winged V-2 of 1945.

Reactance (*X*) is a property of an AC circuit containing capacitance or inductance that together with any resistance makes up its impedance.
The impedance *Z* is given by *Z *^{2} = *R*^{ 2} + *X *^{2}, where *R* is the resistance and *X* is reactance. For a pure capacitance *C*, the reactance
is given by *X _{C}* = 1/2π

*fC*, where

*f*is the frequency of the alternating current; for a pure inductance

*L*,

*X*= 2π

_{L}*f L*. If resistance, inductance, and capacitance are in series the impedance Z = √[R

^{2}+ (

*X*-

_{L}*X*)

_{C}^{2}]. Reactance is measured in ohms.

## Chokes and inductive reactance

Switch a battery across a resistance, and the current in the circuit immediately jumps to its full value (which of course depends
on the voltage supplied by the battery and the resistance in the circuit
according to Ohm's law). But replace the resistance with a *choke* (a large coil of wire), and the current rises *gradually* to its
full value, again determined by the resistance of the coil. Some property
of the coil resists the *change* in current. This property is the
inductance, and the "resistance" of the coil to changing currents is the
inductive reactance.

When a current flows through a wire it sets up a magnetic
field around the wire. As the current rises or falls, the magnetic field
rises or collapses, i.e., it is a *moving* field. When the wire is
coiled into a series of loops the magnetic field around one loop cuts some
of the other loops. Whenever *moving* magnetic fields cut wires,
they generate a difference in electric pressure (i.e., an electromotive
force or e.m.f.) which pushes a current through the wires, provided the
current has a complete circuit to flow around. This is one of the two fundamental
principles of electromagnetism – the generator principle. In the electric
generator a moving coil rotates through a steady magnetic field and makes
a current flow in the wire. A steady field on a moving coil has the same
effect as a moving field on a steady coil – the generation of a current.

So as soon as a current starts to flow round the coil, it makes a growing magnetic field, which generates another separate current. The generated current could flow in either of two directions – in the same direction as the current from the battery or in the opposite direction. If it flowed in the same direction, it would increase the field around the coil, which would generate a bigger current in the adjacent coils, and the process would repeat itself, the current rapidly increasing without limit.

But this is not what we see when the battery is switched across the coil.
In fact, the current slowly builds up to a steady maximum. So the current
must flow in the opposite direction, and tends to *reduce* the *total* current in the coil. The backward current is never as large as the forward
current from the battery, which must win in the end. As the current approaches
its maximum value, it changes more slowly and the back e.m.f. and the backward
current are therefore smaller. When the magnetic field is steady there is
no backward current at all.

The more turns of wire there are in the coil the more turns each turn can affect, or the greater the coil's inductance. Its inductive reactance – the resistance-to-change it offers – is greater.

Inductance affects a DC circuit only when the current is switched on and switched off. Alternating current, on the other hand, is changing its direction, to-and-fro, all the time. The more rapidly the current changes, the more rapidly the magnetic field it makes changes, and the greater will be the inductive reactance which tries to slow down the change.