Circuit – a circuit is a closed loop conducting path in which an electrical current flows.
Common DC Circuit Theory Terms:
• Circuit – a circuit is a closed loop conducting path
in which an electrical current flows.
• Path – a single line of connecting elements or
sources.
• 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.
A Typical DC Circuit
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 Kirchhoff is commonly known as the Conservation of Charge.
We can use Kirchhoff’s current law when analysing parallel circuits.
Kirchhoffs Second Law – The Voltage Law, (KVL)
Kirchhoffs 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 Kirchhoff is known as the Conservation of Energy.
The sum of all the voltages around a loop is
equal to zero.
v1 + v2 + v3 - v4 = 0
We can use Kirchhoff’s voltage law when analysing series circuits.
Problem: Find the current flowing in the 40 Ω Resistor, R3
Soln.: The circuit has 3 branches, 2 nodes (A and B) and 2 independent loops.
Using Kirchhoff’s Current Law, KCL
the equations are given as;
At node A : I1 + I2 = I3
At node B : I3 = I1 + I2
Using Kirchhoff’s Voltage Law, KVL the equations are
given as;
Loop 1 is given as : 10 = R1 I1 + R3 I3 = 10I1 + 40I3
Loop 2 is given as : 20 = R2 I2 + R3 I3 = 20I2 + 40I3
Loop 3 is given
as : 10 – 20 = 10I1 – 20I2
As I3 is the sum of I1 + I2 we can rewrite the above equations as;
Eq. No 1 : 10 = 10I1 + 40(I1 + I2) = 50I1 + 40I2
Eq. No 2 : 20 = 20I2 + 40(I1 + I2) = 40I1 + 60I2
Using equations 1 & 2 we have
I1 = -0.143 Amps
and
I2 = +0.429 Amps
As : I3 = I1 + I2
I3 =
-0.143 + 0.429
I3 = 0.286 Amps
The voltage across the resistor R3 is given as : 0.286 x 40 = 11.44 volts