DE4401&APTE 5601
Topic 3
DC CIRCUITS
KIRCHHOFF’S LAWS
VOLTAGE AND CURRENT DIVIDERS
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In this presentation:
• Introducing:
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Kirchhoff’s Voltage Law
Kirchhoff’s Current Law
Voltage Divider
Current Divider
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Parallel and series circuits: limitations
• Some problems are easily solved by calculating total
parallel or series resistance, but there are many more that
cannot be solved that easily.
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Voltage in series circuit
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Kirchhoff's Voltage Law
• This principle is known as Kirchhoff's Voltage Law
(discovered in 1847 by Gustav R. Kirchhoff, a German
physicist), and it can be stated as such:
• "The algebraic sum of all voltages in a loop must
equal zero“
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Loop
• Starting at any point in the loop continue in the same
direction noting the direction of all the voltage drops,
either positive or negative, until you get back to the
starting point. It is important to maintain the same
direction either clockwise or anti-clockwise or the final
voltage sum will not be equal to zero.
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Branch, Nodes and Loop
• KVL can be used to determine an unknown voltage in a
complex circuit, where all other voltages around a
particular "loop" are known.
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Kirchhoff's Current Law (KCL)
• Kirchhoff's Current Law reads :
• "The algebraic sum of all currents entering and
exiting a node must equal zero"
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Node
• The term Node in an electrical circuit generally refers to
a connection or junction of two or more current carrying
paths or elements such as cables and components. Also
for current to flow either in or out of a node a closed
circuit path must exist.
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KCL example
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Application of KVL and KCL
• Find the current flowing in the 40Ω Resistor, R3
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Voltage divider circuits
• In a simple series circuit, voltage
drop across each resistor is
proportional to its resistance. For
any total voltage, this
proportionality of voltage drops
remains constant.
• For this reason a series circuit is
often called a voltage divider for its
ability to divide the total voltage
into fractional portions of constant
ratio.
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Voltage divider formula
• The ratio of individual resistance to total resistance is the
same as the ratio of individual voltage drop to total
supply voltage in a voltage divider circuit. This is known
as the voltage divider formula
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Voltage Divider General Formula
• The Voltage 𝑉𝑥 across any resistor 𝑅𝑥 in a chain of
resistors in series across a Voltage Source 𝑉𝑇 can be
found from the ratio of that resistance to the Total
resistance
• 𝑉𝑥 =
𝑅𝑥
𝑉𝑇
𝑅𝑇
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Current divider circuits
It is sometimes necessary to find the individual branch currents in
a parallel circuit if the resistances and total current are known, but
the voltage across the resistance bank is not known. When only
two branches are involved, the current in one branch will be some
fraction of the total current. This fraction is the quotient of the
second resistance divided by the sum of the resistances.
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