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Electricity and Magnetism
Lesson 14: KVL
Lesson 14: Kirchhoff’s Voltage Law (KVL)
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Get together in groups of 2 or 4
Arrange your sources and loads in various configurations
For each configuration, measure the voltage across each source and each load
Prove Kirchhoff’s Voltage Law (KVL) by showing that the sum of the voltages around
any circuit is zero
Here are some of the possible configurations of sources and loads (the batteries depicted
below should actually be battery packs with 1 – 4 batteries installed):
NASA-Threads
Electricity and Magnetism
3
V
Source
Lesson 14: KVL
+
VLoad
-
Start
loop
here,
go
around
the
loop
and
return
to
this
point
Experiment with some (or all) of the possible configurations for 2 or 4 battery packs.
For each configuration, record the voltage across each source (battery pack) and each load
(light bulb).
Write a paragraph explaining their observations about each configuration.
Consider the voltage across each source as a positive value and the voltage across each load
as a negative value, with these sign assignments, they should be able to show that the sum
of the voltages around each of their configurations sums to zero volts.
Kirchhoff’s Voltage Law
Due to the conservation of energy, the sum of the voltage sources (taken as positive values)
and the voltage loads (taken as negative values) around any loop in an electrical circuit
sums to zero.
When working KVL problems, we want to consider voltage sources to be positive and
voltage loads to be negative. With that sign
convention, the sum of the voltages around
any loop in a circuit sill be zero.
With that in mind, consider the circuit shown
to the right. If we start in the lower left hand
corner, as indicated, and proceed around the
loop in a clockwise direction, we will end up
back in the lower left hand corner and we
will have encountered one voltage source
and one voltage load along the way.
NASA-Threads
Electricity and Magnetism
Lesson 14: KVL
The source and the load both have polarity markings on them indicating which side of the
element has the higher voltage. As we move around the loop, we can show sources as
positive and loads as negative if we assign each element the polarity we find as we leave
that element.
In this case, as we start in the lower left hand corner and proceed up, we encounter the 3 V
voltage source first. We find the negative polarity sign first as we enter this element and we
find the positive sign as we continue upward and leave this element. So we will assign this
voltage a positive sign value as that is the polarity sign we find as we leave this element. As
we continue around the loop we encounter the load as we move in a downward direction.
We find the positive polarity sign first as we enter this element and the negative polarity
sign as we leave this element, so we will assign this voltage a negative sign.
Applying Kirchhoff’s Voltage Law, the sum of these voltages with these assigned sign values
must be zero.
+3𝑉 + (−𝑉𝐿𝑜𝑎𝑑) = 0
As we solve this equation, we find that the value of VLoad equals +3V.
+3𝑉 − 𝑉𝐿𝑜𝑎𝑑 = 0
+3𝑉 = 𝑉𝐿𝑜𝑎𝑑
To summarize, whenever we use Kirchhoff’s Voltage Law to sum the voltages around a
loop, we must always assign a sign value to each of the voltages. As we proceed around the
loop and encounter the voltage elements, we will find a polarity sign as we enter that
element and another polarity sign as we leave that element. We assign the sign value we
find as we leave that element to the voltage for that element and use that sign value in the
equation we form using Kirchhoff’s Voltage Law.