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Suppose we have this circuit

schematic

simulate this circuit – Schematic created using CircuitLab

How to do nodal analysis for this circuit?

Is it $$5-\frac{5-V_{A}}{2}-V_{A} = 0$$?

or $$5-\frac{5-V_{A}}{2} - 2 \frac{5-V_{A}}{2} = 0$$

EDIT

By

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  • \$\begingroup\$ Notice that 5 has a unit of voltage and (5 - Va)/2 will have a unit of current. So you cannot subtract current from a voltage (subtract apples from bananas). \$\endgroup\$
    – G36
    Jun 14 at 18:04
  • \$\begingroup\$ Yes you are correct. \$\endgroup\$
    – Miss Mulan
    Jun 14 at 18:06

1 Answer 1

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You need to introduce \$I_M\$ into the fray or you'll just get 0 = 0 and that helps nobody: -

$$5 = 2\cdot I_M + V_A$$

Where \$V_A = 2\cdot I_M\$ (as per the dependent source) so: -

$$5 = 2\cdot I_M + 2\cdot I_M$$

And, \$I_M=1.25\text{ amps}\$ and \$V_A = 2.5\text{ volts}\$. Sanity check: -

enter image description here

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