# Dependent source circuit find voltage

Suppose we have this circuit

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

• 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).
– G36
Jun 14 at 18:04
• Yes you are correct. Jun 14 at 18:06

## 1 Answer

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: -