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The Basics of Series Circuits
Simple series circuits can lead to not-so-simple problems
By Ralph Fehr, P.E., Engineering Consultant
Y
ou’re probably familiar
with the old-fashioned
strings of holiday lights
that go out completely if
one bulb burns out. Although these lights cause
hours of frustration during the holidays,
they also provide an excellent example of
a series circuit. The individual bulbs that
make up the string are connected in series, or one after another. When a voltage
is applied across the entire string, a current will flow and the bulbs will light. In
a series circuit, the same quantity of current flows through each element in the
circuit. If a string consists of 60 bulbs, the
applied voltage (120V, for example) is
divided equally across each bulb, resulting in 2V per bulb (120V⫼60 bulbs). The
resistive elements in the bulbs of the series circuit obey Ohm’s Law, which states
that the voltage across a resistive element
equals the resistance of the element times
the current flowing through that element
(V⫽R⫻I).
Series problems. But what happens
when a bulb burns out? When the filament breaks, the series circuit now contains an open link. This open link does
two things: it causes the current to stop
flowing, so the remaining lights go out,
and it causes the full 120V to appear
across the broken filament. This means
that even though the bulbs are designed
to operate at 2V, they have to withstand
120V across the broken filament, which
is clearly a bad design (Figure above).
Modern strings of holiday lights avoid
the “one bad bulb” problem by using a
shorting disk in each bulb that acts as an
open circuit at low, or normal, operating
voltages, but permanently shorts across
the filament when high voltage is impressed across it. An airport runway lighting circuit is another example of a series
circuit. Here, the secondary winding of
82 EC&M May 2003
Holiday lights offer a perfect example of the properties of a series circuit.
an isolation transformer supplies each
bulb. So when a filament burns out, the
primary transformer winding maintains
the series circuit. But even this design
poses a problem.
Too many bad bulbs. Consider again
a 60-bulb light string. If shorting disks
are provided to complete the circuit after
a bulb burns out, what happens if 10
bulbs in the string burn out? The 120V
applied to the string is now divided over
50 bulbs instead of 60, resulting in a voltage of 2.4V per bulb (120V⫼50 bulbs).
This voltage is 20% higher than the design voltage of the bulb, so operating a
60-bulb string of holiday lights with 10
burned out bulbs would shorten the life
of the remaining bulbs considerably. Airport runway lighting circuits avoid this
problem by using constant current power
supplies to supply the series circuit.
Impedance and capacitance. What
if a series circuit consists of elements
other than resistances? Ohm’s Law still
applies, but mathematically it changes
from a basic algebraic equation to a differential equation. This complication is
no cause for panic—it simply means that
for an inductance, the voltage (V) across
the inductor equals the inductance of the
element (L) times the rate at which the
current (i) through the inductance
changes with time.
Similarly, the voltage across a capacitor equals the charge held by the capacitor, which is the current through the capacitor integrated over time, divided by
the capacitance in farads.
The voltage across inductive and capacitive circuit elements requires a current that varies with time. AC currents
vary sinusoidally with time. DC currents,
on the other hand, don’t vary with time,
so inductors and capacitors are short and
open circuits, respectively, to DC. When
DC is switched, however, there is a variation of current with time during the transient period.
As mentioned in the March “Back to
Basics” column on capacitors, a circuit
containing resistance, inductance, and
capacitance is subject to resonance. Resonance is an energy exchange between
the inductor’s magnetic field and the
capacitor’s electric field that produces
high voltages in the process. Sometimes
resonance is a desired condition, such
as in a radio receiver where a tuning circuit is designed to be resonant at the carrier frequency of the radio signal received.
Other times, resonance is undesirable,
as is the case with series capacitors and
the inductance of a long transmission
line where resonance would cause extremely high and potentially damaging
EC&M
voltages.