# current lag and lead

A current flowing around an electric circuit may meet with three different kinds of opposition or impedance. They are caused by resistance (R), inductance (L), and capacitance (C).

Of these, resistance is the easiest to understand, because it has the same
effect on both direct currents and alternating currents. When the voltage across the two terminals of a resistance changes, the current changes immediately.
If the voltage rises, the current rises; and if the voltage falls, the current
falls, and so on. Current and voltage are said to be *in phase*.

Inductors (L) and capacitors (C) behave quite differently. In 'L' circuits
a rise in voltage is accompanied by a rise in current, but this rise is
delayed by a back e.m.f. (see reactance)
generated by the inductor. As the voltage rises and falls, the current rises
and falls, but *a fraction of a second later*. So the current flowing
through the inductor is always lagging behind the voltage, and current and
voltage are said to be *out of phase*.

In 'C' circuits, on the other hand, the current in the circuit must first
flow to the two plates of the capacitor (round the circuit from plate to
plate and *not* across the gap between the plates) to make a potential
difference across them. As the current rises, the voltage between the two
plates rises; and as the current falls, the voltage falls, but *the voltage
follows the current's lead a fraction of a second later*. Current and
voltage are again out of phase, only in 'C' circuits the current is always
leading the voltage.

One complete cycle of an alternating current consists of a rise (in current or voltage) up to the positive maximum, followed by a drop, through zero, to the negative maximum voltage, and a subsequent rise back to the zero starting point. A 'positive' current means that electrons flow in one direction round the circuit, while a 'negative' current means that they surge round in the opposite direction.

In a circuit containing *only resistance*, the positive surges of
current and the positive increases in voltage coincide. But in a circuit
containing *only capacitance* the surges of current occur a quarter
of a cycle *before* the increase of voltage across the capacitance.
In a circuit containing *only inductance* the current surges occur
a quarter of a cycle *later*.

Suppose a capacitor and an inductor are both connected across an alternating
voltage supply (i.e., connected in parallel), then the *same* voltage
sends a current through each. But in the 'C' part of the circuit the current *leads* the voltage and in the 'L' part the current lags behind the
voltage. If the values of inductance and capacitance are selected so that
both offer the same impedance at the frequency of the alternating current
supply, then the current through both 'L' and 'C' parts will be equal. But
since one is a quarter of a cycle behind the voltage, and the other is a
quarter of a cycle in front of the voltage, there is a difference of *phase* of a half cycle between the currents in the 'L' and 'C' parts. As one current
is positive, the other current is negative (i.e., flowing in the opposite
direction) and the same size as the positive current. So the two currents
cancel each other out, and as a result no current flows out of the 'L' and
'C' combination, although there is a voltage connected across the pair of
them. So the inductor-capacitor pair offers a very large impedance to the
current – far larger than their separate impedances.

An arrangement called a parallel tuned circuit or *rejector* circuit will not allow through current of a particular frequency
– the frequency at which the impedance of the capacitor is equal to
the impedance of the inductor. Then the currents flowing through both parts
are equal and opposite in direction. At any other frequency the two impedances
will not be quite equal, the two currents will not be quite cancel each
other out, and some current will be able to flow right round the circuit.