Find I in the circuit


Find I_1 in the circuit.

Find I in the circuit

Image from: Irwin, J. David., and R. M. Nelms. Basic Engineering Circuit Analysis, Tenth Edition. N.p.: John Wiley & Sons, 2010.

Solution:

First, we will pick two nodes to write Kirchhoff’s current law around them (Forgot Kirchhoff’s current law?). They are labeled A and B in the diagram and were arbitrarily picked. We also labeled I_2 as current leaving node A towards node B, which is also labeled in the diagram.

Node B:

I_2+12mA=4mA

I_2=-8mA

(negative because the assumption we made of current leaving node A is wrong, in fact, the current is entering node A in accordance with passive sign convention)

Node A:

2mA=I_1+I_2

2mA=I_1-8mA

I_1=10mA

This question can be found in Basic Engineering Circuit Analysis, 10th edition, chapter 2, question 2.13.

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