CALCULATION OF THE UNKNOWN CURRENT
Welcome with a new quiz from Online Technologies For Beginners (NPROT).
An electrical network with 4 resistors of unspecified value is assigned.
There are also two current generators, one of which has 3 Ampere and one with an unknown value of 3 Ix.
It is requested to calculate the value of Ix in such a way as to have a current equal to 2 Ampere which passes through R3 and a current equal to Ix which passes through R1, according to the directions indicated in the figure.
By applying Kirchhoff’s law of currents at node A, we obtain that the current circulating in R2 must be equal to
3 Ix – Ix = 2 Ix
By applying Kirchhoff’s law of currents to node B, we note that of the 3 A supplied by the current generator, there are 2 A circulating in R3 and 1 A circulating in R2 with the opposite direction to that indicated for 2 Ix.
It follows that:
2 Ix = -1 A.
This reasoning can be formalized by observing that the currents entering B (equal to 2 Ix + 3 A) must equal the current leaving B (equal to 2 A).
So:
2 Ix + 3 = 2
from which, we get that
2 Ix = -1 A.
and therefore
Ix = -0.5 A
which represents the solution of the exercise.
The value obtained allows us to observe that the current generator on the left is delivering a current of 3 Ix = -1.5 A, that is, in the opposite direction to the arrow indicated by the generator symbol.
Ultimately the currents circulating in the circuit are those indicated in blue in the figure.
