I'm pretty stuck trying to solve the below circuit. I need to find the node voltages and branch currents. I've tried it using mesh, nodal and superposition analyses, but I just can't get the right answer. I'm really not sure where I'm going wrong.
Using the mesh analysis, I took the clockwise left-hand loop as x and the clockwise right-hand loop as y.
Then:
$$10V=10I_x+30(I_x-I_y)$$
$$10V=40I_x-30I_y$$
And:
$$6V=40I_y+30(I_y-I_x)+20I_y$$
$$6V=90I_y-30I_x$$
Solving these gives $$I_x=0.4A, I_y=0.2A$$
But I've been told that $$I_x=0.267A, I_y=-0.022A$$
I know my solution is wrong anyway, because I end up with a resistor supplying power to the circuit.
Where am I going wrong?
Best Answer
If you consider the conventional current (current flows from positive node to negative node) your equations are wrong. At the 30Ω resistor the currents actually sum up. So the correct equations are:
$$ 10V=40 I_x + 30 I_y $$
and
$$ 6V=30 I_x + 90 I_y $$
which give the correct answer.