This is a picture of the problem:
Can someone please explain to me, why is to \$V_1=V_2+10\angle{45°}\$ why not \$V_2=V_1+10\angle{45°}\$ or not \$V_1+V_1=10\angle{45°}\$? (It's circled in the picture.)
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3 Answers
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The + and - on the voltage source's symbol are the important factors here. They means that the source is creating a voltage difference such that \$V_1\$ is at a higher voltage than \$V_2\$. Since it's higher by \$10\angle{45°}\$, you have the relationship \$V_1=V_2+10\angle{45°}\$
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As (+)ve node is connected to V1, so V1 should be higher then V2.
But you may think that this voltage source is an ac source as it has phase angle (which is confusing to me cause ac voltage source should have symbol of sin wave, not (+) ve and (-)ve pole ) and so voltage varies from (+)ve to (-)ve and one node will not always be higher then other node, so it should not matter.
You are wrong. Phase angle matter. phase angle of V1 is higher then V2 as V1 = V2+ \$ 10 \angle45 \$. if you do opposite, then V1 's phase will lag and can provide you wrong answer.
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Its simple. Just take V1 ,V2 as sources(just for our understanding purpose) V1 's + sign is connected to '+' sign of 10∠45° voltage source and V2' s + sign is connected to '-' sign of 10∠45°.
Now lets apply kvl for v1 ,v2,10∠45°. Equation will be either \$V1-10∠45°-V2=0\$ or \$V2+10∠45°-V1=0\$ depending on the current directions which we take. Based on these equations we can clearly say \$V1-V2=10∠45°\$. Hope this explanation may clear ur doubt.
