# How did my calculation become Erronous?

So I have this node voltage equation problem. Seems really easy, actually.

simulate this circuit – Schematic created using CircuitLab

In fact, this appears to be only one equation, barring constants. $$\frac{1}{110}v_{12}+(2)\frac{20}{10}+\frac{1}{100}v_1=0$$ with the fairly obvious addition of $v_2=20$.

This works out to be $v_1=200\space\mathrm{v}$.

However, the book says the answer is 219 volts. What is the error in my approach?

• Where is ground? – mkeith Oct 29 '14 at 6:04