Q: Find VO in the circuit of the figure.

A: 96V

Following is my approach to this problem:

I use mesh analysis on 3 the 3 mesh, I determine I1 to be the current flowing through the mesh on the left-lower side of the figure, going clockwise; I2 to be the current going through the mesh on the right-lower side of the figure, going clockwise; I3 to be the current going through the upper mesh going clockwise; and V1 to be the voltage across the primary side of the transformer with the dot side as positive; V2 to be the voltage across the secondary side of the transformer with dot side as positive.

240 = 4I1 + V1
V2 + 10I2 - 2I3 = 0
10I3 - 2I2 = 0 => I2 = 5I3

2V1 = V2
2I2= I1

240 = 8I2 + (1/2)V2
480 = 16I2 + V2

480 - 6I2 - 2I3 = 0
480 - 32I3 = 0

I3 = 480/32 = 15

VO = 15 * 8 = 120V

Please tell me what have I done wrong, thanks!

 

This equation:

10I3 - 2I2 = 0 => I2 = 5I3

is missing V1 and V2. When you go around the I3 loop, you have to include ALL the voltages.

This equation:

2I2= I1

is missing I3. The current in the primary is I1-I3, and the current in the secondary is I3-I2 (don't forget the dot convention as it applies to winding currents); the primary current is twice the secondary current, of course..

Fix those equations and you will have 5 equations in 5 unknowns (I1, I2, I3, V1, V2). You should then be able to get a solution.