Current Sources

In general,
a current source determines the direction and magnitude of the current in the branch where it is located.
Because the current source is not a typical piece of laboratory equipment and has not been employed in the analysis thus far, it will take some time before you are confident in understanding its characteristics and the impact it will have on the network to which it is attached. For the moment, simply keep in mind that a voltage source sets the voltage between two points in a network and the other parameters have to respond to the applied level. A current source sets the current in the branch in which it is located and the other parameters, such as voltages and currents in other branches, have to be in tune with this set level of current.
Fig. 1: Terminal characteristics of an ideal voltage source
Fig. 2: Terminal characteristics of an ideal current source
As shown in [Fig. 1], an ideal voltage source provides a fixed voltage to the network no matter the level of current drawn from the supply. Take note in [Fig. 1] that at every level of current drawn from the supply the terminal voltage of the battery is still E volts.
The current source of [Fig. 2] will establish a fixed level of current that will define the resulting terminal voltage of the attached network as shown in [Fig. 2]. Note that the symbol for a current source includes an arrow to show the direction in which it is supplying the current. Take special note of the fact that the current supplied by the source is fixed no matter what the resulting voltage is across the network. A voltage source and current source are often said to have a dual relationship. The term dual reveals that what was true for the voltage of one is true for the current of the other and vice versa.
the magnitude and the polarity of the voltage across a current source are each a function of the network to which the voltage is applied.
A few examples will demonstrate the similarities between solving for the source current of a voltage source and the terminal voltage of a current source.
Example 1: Find the source voltage, the voltage $V_1$, and current $I_1$ for the circuit in [Fig. 3].
Fig. 3: Circuit for Example 1.
Solution: Since the current source establishes the current in the branch in which it is located, the current $I_1$ must equal I, and
$$I_1 = I = 10 mA$$
The voltage across R1 is then determined by Ohm's law:
$$V_1 = I_1 R_1 = (10 mA)(20 kΩ) = 200 V$$
Since resistor $R_1$ and the current source are in parallel, the voltage across each must be the same, and
$$V_s = V_1 = 200 V$$
with the polarity shown.
Example 2: Find the voltage Vs and currents $I_1$ and $I_2$ for the network in Fig. 4.
Fig. 4: Circuit for Example 2.
Solution: This is an interesting problem because it has both a current source and a voltage source. For each source, the dependent (a function of something else) variable will be determined. That is, for the current source, $Vs$ must be determined, and for the voltage source, Is must be determined.
Since the current source and voltage source are in parallel,
$$Vs = E = 12 V$$
Further, since the voltage source and resistor R are in parallel,
$$V_R = E = 12 V$$
$$I_2 = {V_R \over R} = {12 V \over 4Ω}= 3 A$$
The current $I_1$ of the voltage source can then be determined by applying Kirchhoff's current law at the top of the network as follows:
$$\sum {I_i} = \sum {I_o}$$
$$I = I_1 + I_2$$
$$I_1 = I - I_2 = 7 A - 3 A = 4 A$$

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