A problem in applying Kirchhoff's Voltage Law

AI Thread Summary
The discussion focuses on applying Kirchhoff's Voltage Law (KVL) to a circuit with two loops. The user presents equations derived from the loops, indicating a potential error in calculating current I3, which is approximately 4.63 A. The issue is attributed to the lack of clear current direction labels in the provided diagrams. Participants suggest revising the loop equations while ensuring that current directions are accurately represented. Correctly labeling the currents is essential for obtaining valid results in KVL applications.
Patrick Herp
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Homework Statement
I stumbled upon a question from my little brother's high school textbook (Fig. 1) where the question is the current through R5.
I tried simplifying the circuit into a single loop first before using the properties of resistors in parallel and easy enough, I found it to be I = 0.66... A.

However, apparently, my brother's problem was when he tried to simplify the circuit into a two-loop circuit (Fig. 2) and then applied Kirchhoff's law.

So, to correct his work while also proving that my method is nevertheless correct, I tried applying KCL to his two-loop circuit. That's where the problem begins.
Relevant Equations
Kirchhoff's Voltage Law, Kirchhoff's Current Law, Ohm's Law
Figure 1, Figure 2

1725221267570.png


1725221329643.png


*I'm using his textbook's rule in applying KVL here:
$$
\begin{aligned}
21I_1 + 4.8I_3 &= 100 &&\textrm{Loop I (clockwise)}\\
24I_2 + 4.8I_3 &= 0 &&\textrm{Loop II (clockwise)} \\
I_1 &= I_2 + I_3
\end{aligned}
$$
From the above equations, I get ##I_3 \approx 4.63\textrm{ A}## which is clearly wrong, but I don't know where
 
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I think you'll want to pay attention to the directions of the currents in the two loop circuit. Right now you've got them labelled without directions given.

From your diagram I've put labels on them, such that I1 = I2 + I3:
1725219825923.png

See if you can't write expressions for the two loops, keeping track of the current directions.
 
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