[Solved]

I am attempting the following question:

I first approached it by using a voltage divider around the left-most loop. ie

v = 10/15 x 20 = 13.33V

I looked at the answer in the back of the book (10V) and upon inspection, this seems to be correct, but why is it that the voltage divider approach didn't work?

 

The voltage divider formula didn't work because you failed to reduce the circuit ... but you should have realized that when you stated

... and upon inspection, this seems to be correct, ...

The 10 ohm is in parallel with the series combination of the 4 and 6 ohm resistors.

 

Thank you for your reply, JoeJester. I think the problem here was I was confusing two circuit analysis techniques in my head (KVL and Voltage Divider). I was trying to apply a voltage divider "around any closed circuit." :/