Download EXPERIMENT 3 Kirchoff`s Current Law

İzmir University of Economics
EEE 205 Fundamentals of Electrical Circuits Lab
EXPERIMENT 3
Kirchoff's Current Law
A. Background
In 1845, a German physicist Gustav Robert Kirchhoff stated two
rules regarding the behaviour of electrical circuits.
The first rule, known as Kirchhoff’s Current Law (KCL), is about
the currents entering and exiting a node (junction). KCL states
that “sum of all currents entering and the sum of all currents
leaving a node must be equal”.
i4
i5
i3
i6
i2
i1
Fig.3.1.
Consider the above node given in Fig.3.1.
Currents entering the node = {i1, i2, i4, i6}
Currents leaving the node = {i3, i5}
Therefore KCL states that:
i1 + i2 + i4+ i6 = i3 + i5
Current Division Formula:
Consider the circuitry given in Fig.3.2.
i0
i1
R1
+
V
-
i2
R2
Fig.3.2.
3-1
For the upper node, i0 is the entering current and i1 and i2 are the leaving
currents. Then
i0 = i1 + i2
The voltage drops over the resistors are equal, then
R1 i1 = R2 i2
Solving the above two equations simulatenously, the brach currents i1 and i2
can be expressed in terms of the incoming total current i0 as:
i1 =
R2
i
R1 +R2 0
i =
R
i
R1 +R2 0
and
3-2
B. Preliminary Work
1. Consider the circuit given in Fig. 3.3.
18 kΩ
i1
i2
i0
22 kΩ
10 V
i3
10
kΩ
i4
2.2
kΩ
Fig.3.3.
1.1. Express the currents i1 and i2 in terms of the currents i0, using current
division rule.
1.2. Similarly express the currents i3 and i4 in terms of the currents i0,
using the current division rule.
1.3. Determine the currents i1, i2, i3, i4, and i0. (The students who have
different and unique solutions will get extra credits)
1.4. Using the solutions, determine the ratios
i
1 i
and
i2
i
1.5. Compare your check with your theoretical calculations in part 1.1.
1.6. Using the solutions, determine the also ratios
i3
i
and
i4
i
1.7. Compare your check with your theoretical calculations in part 1.2.
3-3
C. Experimental Work
1.
Firstly attach the Y-0016/002 modul on your experiment set. Make the
circuit connections as in given Fig. 3.4.
Fig 3.4
1.1
Apply the voltages given below to your circuit respectively and
measure the current values for every step. Write your
measurements onto the Table 3.1.
Table 3.1.
E (Volts)
I1 (mA)
I2 (mA)
I3 (mA)
I (mA)
I1+I2+I3 (mA)
1
2
3
4
5
1.2
Are the currents entering and the currents leaving equal? Is KCL
dependent on currents and voltage values?
3-4
2.
Now contruct the circuit you have studied in Preliminary work (Fig.3.5)
i1 …… kΩ
i2
R1 R
2
...… kΩ
10 V
i0
i3
…..
kΩ
R3
R4
i4
…..
kΩ
Fig 3.5
2.1.
Before you contruct the circuit, determine the values of the
resistors using (i) color codes, (ii) ohmmeter of your multimeter
and fill in Table 3.2. Write down the measured values on Fig. 3.5.
Table 3.2.
R1=18 kΩ
Color Code
R2=22 kΩ
Measured
Color Code
R3=10 kΩ
Color Code
2.2.
Measured
R4=2.2 kΩ
Measured
Color Code
Measured
Contruct your circuit and do the measurements. Write your
findings in Table 3.3.
Table 3.3.
i1 (mA)
2.3.
i2 (mA)
i3 (mA)
i4 (mA)
i0 (mA)
Verify KCL at all nodes.
3-5
2.4.
Verify current division rule for the currents i1, i2, i3, and i4.
Compare theoretical expectations and measurement results.
3-6