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The Basics of Parallel Circuits
Components in parallel share current,
but not necessarily equally
By R. Fehr, P.E., Engineering Consultant
L
ast month’s column covered
the behavior of electrical components connected in series
and demonstrated that when
a voltage is applied across a
series circuit, the current
through each component is the same.
However, you’ll often come across components connected in parallel, a configuration that changes the behavior of the
circuit and the currents that flow through
each component.
Paralleling components. When components are connected in parallel, the
voltage across each element is equal. The
current flowing through each element,
however, isn’t necessarily equal. Current
divides through the elements based on
their individual impedances, seeking the
path of least resistance. Elements with
high impedances carry less current than
elements with low impedances. Sometimes two elements put in parallel need
to share the current equally, as is usually
the case with paralleled transformers. To
achieve equal sharing of the current, it’s
necessary that the impedances of each
element be equal.
The resistance in the capacitive branch of practical tuning circuits is negligible, but the windings of the conductor can create considerable resistance in the inductive branch.
Analyzing the units of measurement, one
can see that current flowing through an
inductor represents the energy stored by
the inductor per coulomb of charge passing through the inductor. Similarly, the
current flowing through a capacitor
equals the time rate of change of the voltage across the capacitor multiplied by the
capacitance (C) in farads (F), or
of the inductor. For the circuit shown in
the Figure, if the inductance is 10 mH,
what size capacitor must be used to cause
the circuit to be resonant at 20.6 kHz?
To achieve resonance, the inductive and
capacitive reactances must be equal, or
Substituting values yields
Inductance and capacitance. Just
like with a series circuit, if a parallel circuit consists of elements other than resistances, the basic algebraic equations
describing the current flowing in each
branch of the circuit become differential
equations. In the case of an inductance, the
current (I) flowing through the inductor
equals the voltage across the inductor integrated over time divided by the inductance (L) of the element in henrys, or
78 EC&M June 2003
Resonance. As with series circuits containing resistances, inductances, and capacitances, if the inductive reactance of
a parallel circuit equals the capacitive reactance, the circuit is said to be resonant
at that frequency. A common example of
parallel resonance is a tuning circuit, as
shown in the Figure above.
In practical tuning circuits, the resistance in the capacitive branch is negligible, but the inductive branch has a considerable resistance due to the windings
To finish, solve for C
or
The combination of the 10 mH inductor and the 6,000 pF capacitor is resonant
at 20.6 kHz only. For any other frequency,
the two reactances won’t be equal, so resoEC&M
nance won’t occur.