Why Does I Appear in the Voltage Equation for Parallel Circuits?

[sparkle123]

I don't understand how I comes into play in the four equations.
For example, in V = (I + I₁)R, shouldn't it just be
V = I₁R?
Or V = (I_{(component through bottom wire)} + I₁)R?

Any help would be greatly appreciated. Thanks!

 

[gneill]

Imagine that there's another loop involved, one that is supplying the voltage V and current I at the given nodes:

I think you'll see where the "I" is coming from.

 

[sparkle123]

Thank you very much! But isn't the I split between the three branches instead of going entirely through the bottom one? Thanks again!

 

[sparkle123]

Oh I get it - thank you! :)