Confusion over sign convention for power

We are given this electrical circuit:

At the last line, they put a 'minus'.

My question is, why is it a minus?

• Consumer consensus? – Matt Young Feb 29 '16 at 3:07
• @MattYoung That was a free translation from my native language. I meant Passive sign convention! – Sijaan Hallak Feb 29 '16 at 12:15

1 Answer

Because whoever drew the circuit is adhering to the passive sign convention, which states that active devices that source power have a negative power term, and passive devices that sink power have a positive power term.

Resistance is always positive, any real quantity squared is positive, and therefore $RI_S^2$ must be a positive quantity. Consequently, $-12\cdot RI_S^2$ must be a negative quantity; the negative is added to adhere to the convention.