I am having trouble with this problem. It seems simple but I am new to KVL so I may be doing something stupid. Please take a look at the attachment and let me know what I'm doing incorrectly as they both seem to be valid equations to the circuit. Thanks a bunch!

 

I am having trouble with this problem. It seems simple but I am new to KVL so I may be doing something stupid. Please take a look at the attachment and let me know what I'm doing incorrectly as they both seem to be valid equations to the circuit. Thanks a bunch!View attachment 146083

Here's a little hint I was taught in high school, and I still use it. It's called RED before BLACK. Imagine you have a voltmeter, with one black lead, and one red lead. Measure each voltage drop as you move around the loop with the RED lead always in front of the BLACK lead. Notice that, when you're across the battery, you will read a positive polarity. But when you go across the resistors, you will read a negative polarity! This has always helped me keep the signs correct.

 

You know that (a) is correct, i.e. Vc - Va - Vb = 0.
So you just need to apply Ohm's law to get Vc, Vb and substitute them into the equation above to get the result.

In (b) your Vb expression is wrong. You need to check the sign again.

 

Write Va, Vb, and Vc in terms of the supply voltage or in terms of the current Ic and the resistances. Then substitute into the first equation.

Of course, if they don't match, that doesn't tell you which one is wrong, but once you see that they are different, you should be able to verify which one is correct quickly.

 

Thanks everyone! This is my first time using this site and you all have been very helpful and expedient!