Question
Download Solution PDFDetermine the current ia in the given network
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Kirchoff's Current Law (KCL): The algebraic sum of the currents at a node is zero. Alternatively, the sum of the currents entering a node is equal to the sum of the currents leaving that node.
I1 - I2 - I3 + I4 + I5 = 0
Calculations:
Circuit Diagram:
Here, ia is given by,
\({i_a} = \frac{{{V_x} - 12}}{4}\) ...(1)
Apply KVL at node Vx,
\(\frac{{{V_x} - 12}}{4} + 3{i_a} + \frac{{{V_x}}}{2} = 0\)
Put the value of ia in above equation,
\(\frac{{{V_x} - 12}}{4} + 3\left( {\frac{{{V_x} - 12}}{4}} \right) + \frac{{{V_x}}}{2} = 0\)
\(\frac{{{V_x} - 12}}{4} + \frac{{3{V_x} - 36}}{4} + \frac{{{V_x}}}{2} = 0\)
Vx - 12 + 3Vx - 36 + 2Vx = 0
6 Vx = 48
Vx = 8 V
Put this value of V in equation (1)
ia = (8 - 12) / 4 = -1 A
Last updated on May 29, 2025
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