logistic_guy
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Solve for the current flowing through the \(\displaystyle 8\)-\(\displaystyle \Omega\) resistor.
DC circuit
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logistic_guy
Senior Member
- Joined
- Apr 17, 2024
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Let the node that connects the three resistors have \(\displaystyle v_1\), then by nodal analysis we have:
\(\displaystyle \frac{v_1 - 5}{2} + \frac{v_1 - 0}{8} + \frac{v_1 + 3}{4} = 0\)
Or
\(\displaystyle 4v_1 - 20 + v_1 + 2v_1 + 6 = 0\)
\(\displaystyle 7v_1 = 14\)
\(\displaystyle v_1 = 2 \ \text{V}\)
Then,
\(\displaystyle i_{8\Omega} = \frac{v_1}{8} = \frac{2}{8} = \frac{1}{4} = 0.25 \ \text{A}\)
\(\displaystyle \frac{v_1 - 5}{2} + \frac{v_1 - 0}{8} + \frac{v_1 + 3}{4} = 0\)
Or
\(\displaystyle 4v_1 - 20 + v_1 + 2v_1 + 6 = 0\)
\(\displaystyle 7v_1 = 14\)
\(\displaystyle v_1 = 2 \ \text{V}\)
Then,
\(\displaystyle i_{8\Omega} = \frac{v_1}{8} = \frac{2}{8} = \frac{1}{4} = 0.25 \ \text{A}\)