Consider the configuration shown in the figure which is a portion
Consider the configuration shown in the figure which is a portion of a larger electrical network
For R = 1 Ω and currents i1 = 2 A, i4 = -1 A, i5 = -4 A. Which one of the following TRUE?
A. i<sub>6</sub> = 5 A
B. i<sub>3</sub> = -4A
C. Data is sufficient to conclude that the supposed currents are impossible
D. Data is insufficient to identify the currents i<sub>2</sub>, i<sub>3</sub>, and i<sub>6</sub>
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Concept:
According to Kirchhoff’s current law (KCL), the algebraic sum of the electric currents meeting at a common point is zero.
Mathematically we can express this as:
\(\mathop \sum \limits_{n = 1}^M {i_n} = 0\)
Where in represents the nth current
M is the total number of currents meeting at a common node.
KCL is based on the law of conservation of charge.
Application:
Given: i1 = 2A, i4 = -1 A, i5 = -4A
KCL at Node ‘A’:
i4 + i1 = i2
i2 = 2 – 1
i2 = 1 A
KCL at Node ‘B’:
i2 + i5 = i3
i3 = 1 – 4
i3 = -3A
KCL at Node ‘C’:
i3 + i6 = i1
i6 = 2 – (-3)
i6 = 5 A
