- #1
Patrick Herp
- 5
- 0
- 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
*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
*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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