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I understand that passive convention in circuit analysis is when current flows in through the positive terminal of a resistor, thus indicating that the element is absorbing energy as shown in the diagram below. The value of the current is also positive in this direction.

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However, if the direction of the current in the above diagram is reversed, it is no longer obeying passive convention and the value of the current would be negative. Does this now mean that it is supplying power to the voltage supply? If so, doesn't it still have to absorb power while the current is entering from the negative terminal of the resistor?

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I'm having a little trouble parsing your multiple negatives, so let me just try to clarify the passive sign convention.

The PSC says that current enters the element's terminal that is assumed to have the higher voltage. If you define an element's current and voltage in this way then you can apply these equations: $$ V = IR \qquad P = VI$$ Now it may turn out that the actual value of the voltage or current is negative, and that is not a problem. If you ignore the PSC and define the current as entering the terminal that is assumed to have the lower voltage, then you have to use: $$ V = -IR \qquad P = -VI$$ Here's where it gets tricky. A current with a negative value entering the negative voltage terminal is exactly equivalent to a current with a positive value entering the positive voltage terminal.

If you are following the PSC when defining the current through and voltage across a resistor, then it must be true that their values are either both positive or both negative. A resistor's power must be positive, meaning that a resistor always consumes power.

For an ideal voltage or current source, the calculated power can be either positive or negative. If negative, it means that the source is providing power to the circuit. If positive, the source is consuming power (like a battery being charged).

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