negative voltage sources and KVL

Question

I have the following circuit:

^{simulate this circuit – Schematic created using CircuitLab}

If I choose clockwise current direction then KVL gives me: $$10\text{V}+5\text{k}\Omega \times I-0.7=0 \rightarrow I=-1.86\text{mA}$$ If I choose counter clockwise current direction KVL gives me: $$-10\text{V}+5\text{k}\Omega \times I+0.7=0 \rightarrow I=+1.86\text{mA}$$

I want to ask if I am doing something wrong or the negative current in the first case is because the assumed current direction is backwards to the actual flow?

Answer 1

Nope, you're absolutely correct in both cases. A negative magnitude of a vector is the same as a positive magnitude on the vector in the opposite direction.

Answer 2

What you have done is perfectly correct , to have a better clarification check the image below