Lesson #3: Main Circuit Laws
1- Kirchhoff's circuit laws:
In 1845, a German physicist, Gustav Kirchoff developed a pair or set of rules or laws which
deal with the conservation of current and energy within electrical circuits. These two rules are
commonly known as: Kirchhoff’s Circuit Laws with one of Kirchhoff’s laws dealing with the
current flowing around a closed circuit, Kirchhoff’s Current Law, (KCL) while the other law
deals with the voltage sources present in a closed circuit, Kirchhoff’s Voltage Law, (KVL).
Kirchhoff’s First Law - the Current Law, (KCL)
Kirchhoff’s Current Law or KCL, states that the "total current or charge entering a junction
or node is exactly equal to the charge leaving the node as it has no other place to go except to
leave, as no charge is lost within the node". In other words the algebraic sum of ALL the
currents entering and leaving a node must be equal to zero, I(exiting) + I(entering) = 0. This idea by
Kirchoff is commonly known as the Conservation of Charge.
Kirchhoff’s Current Law:
Here,
the
3
currents
entering
the
node, I1, I2, I3 are all positive in value and the 2
currents leaving the node, I4 and I5 are negative
in value. Then this means we can also rewrite
the equation as;
I1 + I 2 + I 3 - I 4 - I 5 = 0
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. We can use Kirchhoff’s current
law when analyzing parallel circuits.
Kirchhoff’s Second Law - the Voltage Law, (KVL)
Kirchhoff’s Voltage Law or KVL, states that "in any closed loop network, the total voltage
around the loop is equal to the sum of all the voltage drops within the same loop" which is also
equal to zero. In other words the algebraic sum of all voltages within the loop must be equal to
zero. This idea by Kirchoff is known as the Conservation of Energy.
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Lesson #3: Main Circuit Laws
Kirchhoff’s Voltage Law:
Starting at any point in the loop continue
in the same direction noting the direction
of all the voltage drops, either positive or
negative, and returning back to the same
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. We can use
Kirchhoff’s voltage law when analyzing series circuits.
When analyzing either DC circuits or AC circuits using Kirchhoff’s Circuit Laws a number
of definitions and terminologies are used to describe the parts of the circuit being analysed
such as: node, paths, branches, loops and meshes. These terms are used frequently in circuit
analysis so it is important to understand them.
Circuit - a circuit is a closed loop conducting path in which an electrical current flows.
•
Path: a line of connecting elements or
sources with no elements or sources
included more than once.
•
Node: a node is a junction, connection
or terminal within a circuit were two
or more circuit elements are connected
or joined together giving a connection
point between two or more branches.
A node is indicated by a dot.
•
Branch: a branch is a single or group
of components such as resistors or a source which are connected between two nodes.
•
Loop: a loop is a simple closed path in a circuit in which no circuit element or node is
encountered more than once.
•
Mesh: a mesh is a single open loop that does not have a closed path. No components are inside
a mesh.
2- Ohms Law
The relationship between Voltage, Current and Resistance in any DC electrical circuit was
firstly discovered by the German physicist Georg Ohm, (1787 - 1854). Georg Ohm found that,
at a constant temperature, the electrical current flowing through a fixed linear resistance is
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Lesson #3: Main Circuit Laws
directly proportional to the voltage applied across it, and also inversely proportional to the
resistance. This relationship between the Voltage, Current and Resistance forms the bases
of Ohms Law and is shown below.
Ohms Law Relationship
Current( I ) =
Voltage(V )
in Amperes( A )
Resistance( R )
By knowing any two values of the Voltage, Current or Resistance quantities we can use Ohms
Law to find the third missing value. Ohms Law is used extensively in electronics formulas
and calculations so it is "very important to understand and accurately remember these
formulas".
To find the Voltage, ( V )
[V=I × R]
V (volts) = I (amps) × R ( Ω )
To find the Current, ( I )
[I=V÷R]
I (amps) = V (volts) ÷ R ( Ω )
To find the Resistance, ( R )
[R=V÷I]
R ( Ω ) = V (volts) ÷ I (amps)
Review:
1- Kirchhoff's First Law says that:
A. Total current flowing into a point is the same as the current flowing out of that point.
B. Current loses strength as it flows about a circuit.
C. Voltage loses strength as it flows about a circuit.
D. Wires need insulation to stop electrons from leaking out of the wire.
E.
2- Kirchhoff's Second Law states
A. Sum of the potential differences is less than the battery voltage.
B. The sum of the potential differences is dependent on the route taken by the current.
C. The sum of potential differences throughout the circuit adds up to zero, regardless of the route
taken.
D. The sum of potential differences throughout the circuit adds up to zero, but only if the
components are in Resistors.
3- A Voltage of 9 Volts is placed across a 27 ohm resistor. What current flows through the resistor?
A. 3 amperes
B. 0.33 amperes
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Lesson #3: Main Circuit Laws
C. 243 amperes
D. 18 amperes
4- If the resistance in a circuit increases while the voltage stays the same, what happens to the current?
A.
B.
C.
D.
The current stays the same
The current increases
The current decreases
The current oscillates
5- Ohm's Law states that the current in a circuit is:
A.
B.
C.
D.
inversely proportional to the resistance.
directly proportional to the resistance.
inversely proportional to the square of the resistance.
independent of resistance.
6- Ohm's Law states that the current in a circuit is:
A.
B.
C.
D.
inversely proportional to the voltage
inversely proportional to the square of the voltage
inversely proportional to the squareroot of the voltage
directly proportional to the voltage
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