Question

help me solve this nodal analysis
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Answer 1

Answer on Question #61198-Engineering-Electrical Engineering

Help me solve this nodal analysis

3.15 Apply nodal analysis to find i0 and the power dissipated in each resistor in the circuit.

Solution

Nodes 1 and 2 form a supernode so that $v_{1} = v_{2} + 10$ (1)

At the supernode, $2 + 6v_{1} + 5v_{2} = 3(v_{3} - v_{2}) \rightarrow 2 + 6v_{1} + 8v_{2} = 3v_{3}$ (2)

At node 3, $2 + 4 = 3(v_{3} - v_{2}) \rightarrow v_{3} = v_{2} + 2$ (3)

Substituting (1) and (3) into (2),

$$2 + 6 v _ {2} + 6 0 + 8 v _ {2} = 3 v _ {2} + 6 \rightarrow v _ {2} = - \frac {5 6}{1 1} = - 5. 1 V$$ $$v _ {1} = v _ {2} + 1 0 = \frac {5 4}{1 1} = 4. 9 V$$ $$i _ {0} = 6 v _ {1} = 2 9. 4 5 A$$ $$P _ {6 5} = v _ {1} ^ {2} G = \left(\frac {5 4}{1 1}\right) ^ {2} 6 = 1 4 4. 6 W$$ $$P _ {5 5} = v _ {2} ^ {2} G = \left(- \frac {5 6}{1 1}\right) ^ {2} 5 = 1 2 9. 6 W$$ $$P _ {3 5} = (v _ {2} - v _ {3}) ^ {2} G = (2) ^ {2} 3 = 1 2 W$$

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