How to calculate the voltage V0 across the 8ohm resistor? Using mesh analysis I get an answer(120V) which is different from the correct answer.

Left loop, $$4I_1+V_1=120$$ Right loop, $$10I_2+2I_3+V_2=0$$ Outer loop, $$-120+4I_1+8I_3-8I_2=0$$

Solving I get, $$I_3=15A \text{ and }V_0=120V$$

  • 1
    \$\begingroup\$ Is any data given about the transformer? Pleas edit the question to show the steps that you have followed. \$\endgroup\$
    – AJN
    Nov 28, 2020 at 7:48
  • \$\begingroup\$ Also, please use MathJax to format equations nicely. Make clear your effort up to point stuck and ask help to get unstuck, not expecting free homework service. \$\endgroup\$ Nov 28, 2020 at 11:09
  • \$\begingroup\$ Which 8 ohm resistor? \$\endgroup\$
    – Hot Licks
    Nov 28, 2020 at 15:52
  • \$\begingroup\$ @HotLicks The one which is connected to both primary and secondary side. And \$V_0\$ is the voltage across the resistor. \$\endgroup\$ Nov 29, 2020 at 12:01

1 Answer 1


I suspect the transformer is ideal, and it is where you may be stuck. Current into a polarity dot on one side means current out of the dot on other side. Their magnitude will be exactly per turns ratio.

So, draw an arrow going into left side dot and assign it a current variable. Then draw an arrow coming out of the other dot (or in to non-polarity dot side if easier) and assign it the same current variable, but scale it by \$1/2\$. Also, assign a voltage variable to one side, scale it and assign with appropriate polarity on the other side as well. Then you can write KVL and KCL equations to solve.

enter image description here

Below I have assigned variables that should help you write the needed equations,

enter image description here

  • \$\begingroup\$ I'm able to find the current flowing in the secondary winding. But I'm confused about the voltage across the 8ohm resistor because it is connected to both primary and the secondary winding. Should I consider another current I3 and solve for it? \$\endgroup\$ Nov 28, 2020 at 11:40
  • \$\begingroup\$ Yes, and it will fit nicely into the two node equations. Also add voltage variable across your transformer to help you write KVL equations. I added a picture to clarify. \$\endgroup\$ Nov 28, 2020 at 12:10
  • \$\begingroup\$ How should I take the equation for 8ohm resistor connected to both primary and secondary circuit? Should V1 and V2 be included in the equation? \$\endgroup\$ Nov 28, 2020 at 12:37
  • \$\begingroup\$ I would write KVL equations for left loop, right loop, and then an overall loop around perimeter of entire circuit. That, with the two node equations should suffice. You can edit your question to show us your equations. \$\endgroup\$ Nov 28, 2020 at 12:45
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    \$\begingroup\$ See if my edit (added circuit with suggested variables) helps. The current up through the bottom right 8Ω resistor (from KCL) is \$\frac{i_2}{2}+i_3\$. \$\endgroup\$ Nov 28, 2020 at 14:24

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