Basic Concepts of Electrical Circuits

Power of Independent Sources

Determine the power of each source.
a)
Voltage and Current Sources
b)
Voltage and Current Sources

Solution
a) The current source keeps the current of the loop 2A and the voltage source keeps the voltage across the current source 3v as shown below.
Voltage and Current Sources
For the voltage source the current enters from the positive terminal. Therefore, the passive sign convention should be used to find the sign of power:
P=V \times I= 3 \times 2 =6W > 0 absorbing power
For the current source, the current leaves from the positive terminal. Hence, the active sign convention should be used:
P= - V \times I= - 3 \times 2 =-6W < 0 supplying power
b) Similarily, the voltage across the current source and the currentpassing through thevoltage source can be easily determined by voltage and current sources, respectively:
Voltage and Current Sources
For this problem, the current enters to the voltage source from the negative terminal. Thus, the active sign convention should be used:
P=-V \times I= -3 \times 2 =-6W 0 absorbing power


 Current of A Voltage Source
Find the current passing through the voltage source:
a)
A voltage source in series with a current source
b)
A voltage source in series with a current source and other elements

Solution
a) The voltage source is in series with the current source. Since by definition a current source keeps the current passing through itself constant and the voltage source is in series with the current source, it should have the same current 10 A.
A voltage source in series with a current source
b) The same scenario is happening here and the voltage source has the same current as the current source 5A.
A voltage source in series with a current source and other elements


Voltage of A Current Source

Find voltages across the current sources.
a)
A Current Source Parallel with A Voltage Source
b)
Voltage Across Parallel Elements
c)
Parallel Current and Voltage Sources
d)
Parallel Current and Voltage Sources
e)
Parallel Current and Variable Voltage Sources

Solution
In each case, the current source is parallel with a voltage source. Therefore, the voltage across the current source is equal to the voltage of the voltage source, regardless of other elements.
a)
A Current Source Parallel with A Voltage Source
b)
Voltage Across Parallel Elements
c)
Parallel Current and Voltage Sources
d)
Parallel Current and Voltage Sources
e)













Parallel Current and Variable Voltage Sources

Elements, Nodes, Loops and Branches

How many elements / nodes / loops / branches does the following circuit have?

Solution
8 elements
6 nodes, as shown:

7 loops, as shown:

8 branches

Using Power and Conductance

Determine the resistance of the resistor, I and V.

Solution
R=\frac{1}{G}=2 \Omega,\, P=RI^2\rightarrow I=\sqrt{\frac{P}{R}}=\pm\sqrt{5} A .
There are two answers:
a) I=+\sqrt{5} A\rightarrow V=RI=+2\sqrt{5} .
b) I=-\sqrt{5} A\rightarrow V=RI=-2\sqrt{5} .


Power and Conductance of Resistors

Determine the power absorbed by the resistors, the conductance of the resistors and V .


Solution
a) P=RI^2=40W, V=RI=20 v, G=\frac{1}{R}=0.1 S.
b) P=RI^2=40W, V=RI=-20 v, G=\frac{1}{R}=0.1 S.

Power of Elements

Find the power of each element. Which one is supplying power and which one is absorbing it?
Power of Elements

Solution
a)  Passive sign convention, P = V \times I = -8 W < 0 supplying power.
b)  Passive sign convention, P = V \times I = 8 W > 0 absorbing power.
c)  Passive sign convention, P = V \times I = 20 W > 0 absorbing power.
d)  Active sign convention, P = - V \times I = - 50 W < 0 supplying power.




 


 


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