kirchoff's law problems with solution
Kirchhoff law definition and principle
The sum of the currents flowing into a point in a circuit is equal to the sum of the currents flowing out of that same point.In addition to providing the voltage law for series circuits, Gustav Kirchhoff (in 1847) was the first to observe and prove that the sum of all the branch currents in a parallel circuit (I1 + I2 + I3, etc.) was equal to the total current (IT). In honor of his second discovery, this phenomenon is known as Kirchhoff’s current law, which states that the sum of all the currents entering a junction is equal to the sum of all the currents leaving that same junction.
Figure 4-8(a) and (b) illustrate two examples of how this law applies. In both examples, the sum of the currents entering a junction is equal to the sum of the currents leaving that same junction. In Figure 4-8(a) the total current arrives at a junction X and splits to produce three branch currents, /1 I2, and I3, which cumulatively equal the total current (IT) that arrived at the junction X. The same three branch currents combine at junction Y, and the total current (Jr) leaving that junction is equal to the sum of the three branch currents arriving at junction Y Stated mathematically:
Kirchhoff law formula
Problem law N°1
Refer to Figure 2 and calculate the value of IT.
Solution 1 :
By Kirchhoff’s current law,IT = I1 + I2 + I3 + I4
IT = 2 mA + 17 mA + 7 mA + 37 mA
Problem N°2
Refer to Figure 3 and calculate the value of IT
Solution 2 :
By transposing Kirchhoff’s current law, we can determine the unknown value (IT):IT = I1 + I2
7A = x + 3A
I1 = 4A
OR
IT = I1 +I2
IT - I2 = I1
I1 = IT - I2 = 7A - 3A =4A