We are given this electrical circuit:

enter image description here

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

My question is, why is it a minus?

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

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.


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