Kirchhoff's Laws are fundamental principles in electrical circuit theory that govern the behavior of electrical circuits, specifically in terms of current and voltage. They are named after Gustav Kirchhoff, a German physicist who formulated them in the mid-19th century.
1. **Kirchhoff's Current...
6/11/24, 8:30 PM Kirchhoff's Current And Voltage Law
Kirchhoff’s Voltage Law:
Kirchhoff’s Voltage Law (KVL) is Kirchhoff’s second law that deals
with the conservation of energy around a closed circuit path.
Gustav Kirchhoff’s Voltage Law is the second of his fundamental laws
we can use for circuit analysis. His voltage law states that for a closed
loop series path the algebraic sum of all the voltages around any
closed loop in a circuit is equal to zero. This is because a circuit loop
is a closed conducting path so no energy is lost.
In other words the algebraic sum of ALL the potential differences
around the loop must be equal to zero as: ΣV = 0. Note here that the
term “algebraic sum” means to take into account the polarities and signs
of the sources and voltage drops around the loop.
This idea by Kirchhoff is commonly known as the Conservation of
Energy, as moving around a closed loop, or circuit, you will end up
back to where you started in the circuit and therefore back to the same
initial potential with no loss of voltage around the loop. Hence any
voltage drops around the loop must be equal to any voltage sources met
along the way.
So when applying Kirchhoff’s voltage law to a specific circuit element,
it is important that we pay special attention to the algebraic signs,
(+ and -) of the voltage drops across elements and the emf’s of sources
otherwise our calculations may be wrong.
But before we look more closely at Kirchhoff’s voltage law (KVL) lets
first understand the voltage drop across a single element such as a
resistor.
A Single Circuit Element
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,6/11/24, 8:30 PM Kirchhoff's Current And Voltage Law
For this simple example we will assume that the current, I is in the same
direction as the flow of positive charge, that is conventional current
flow.
Here the flow of current through the resistor is from point A to point B,
that is from positive terminal to a negative terminal. Thus as we are
travelling in the same direction as current flow, there will be a fall in
potential across the resistive element giving rise to a -IR voltage drop
across it.
If the flow of current was in the opposite direction from point B to
point A, then there would be a rise in potential across the resistive
element as we are moving from a - potential to a + potential giving us
a +I*R voltage drop.
Thus to apply Kirchhoff’s voltage law correctly to a circuit, we must
first understand the direction of the polarity and as we can see, the sign
of the voltage drop across the resistive element will depend on the
direction of the current flowing through it. As a general rule, you will
loose potential in the same direction of current across an element and
gain potential as you move in the direction of an emf source.
The direction of current flow around a closed circuit can be assumed to
be either clockwise or anticlockwise and either one can be chosen. If the
direction chosen is different from the actual direction of current flow,
the result will still be correct and valid but will result in the algebraic
answer having a minus sign.
To understand this idea a little more, lets look at a single circuit loop to
see if Kirchhoff’s Voltage Law holds true.
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, 6/11/24, 8:30 PM Kirchhoff's Current And Voltage Law
A Single Circuit Loop
Kirchhoff’s voltage law states that the algebraic sum of the potential
differences in any loop must be equal to zero as: ΣV = 0. Since the two
resistors, R1 and R2 are wired together in a series connection, they are
both part of the same loop so the same current must flow through each
resistor.
Thus the voltage drop across resistor, R1 = I*R1 and the voltage drop
across resistor, R2 = I*R2 giving by KVL:
We can see that applying Kirchhoff’s Voltage Law to this single closed
loop produces the formula for the equivalent or total resistance in the
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