# Node voltage equation with weird solutions

I recently had an exam with the following multiple choice problem:

Consider the circuit below:

The node voltage equation for node A is which of the following?:

1. $$\ \frac{V_A-kV_a}{R_1}+ \frac{V_A-V_3}{R_2} + \frac{V_A-V_B}{R_6} = 0 \$$
1. $$\ \frac{V_A+kV_A}{R_1} + \frac{V_A-V_3}{R_2} + \frac{V_A-V_B}{R_6} = 0 \$$
1. $$\ \frac{V_A-kV_A}{R_1} + \frac{V_A+V_3}{R_2} + \frac{V_A+V_B}{R_6} = 0 \$$
1. $$\ \frac{V_A+kV_A}{R_1} + \frac{V_A+V_3}{R_2} + \frac{V_A+V_B}{R_6} = 0 \$$
1. $$\ \frac{2V_A}{R_1} + \frac{V_A+V_3}{R_2} + \frac{V_A+V_B}{R_6} = 0\$$
1. $$\ \frac{V_A-V_3}{R_2} + \frac{V_A-V_B}{R_6} = 0\$$

My attempt

This is how I would make the node voltage equation for node A:

$$\ \frac{V_A}{R_1} + \frac{V_A-V_3}{R_2} + \frac{V_A-V_B}{R_6} + ki_1 = 0 \$$

But as you can see, it doesn't match any of the options above and I can't figure out how I'm supposed to reach on of those solutions.

Can somebody help me out?

• fix i1 to i2 in your eq.
– user136077
Commented Jun 14, 2020 at 9:00