The junction rule states that the net current entering a junction must equal the net current leaving the junction. We define the direction of the current to be the direction of flow of positive charges.

Moving from negative to positive through a battery causes positive charge carriers to gain potential, while moving from positive to negative causes them to lose potential.

The script E stands for electromotive force (EMF) and equals the potential difference across the battery for an ideal battery. This assumes there is no internal resistance in the battery.

Moving through a resistor in the direction of the current causes the charges to lose potential.

First we define change in potential energy in terms of the EMF of the battery. Power is the time derivative of potential energy, which can be written in terms of current and EMF. Power in a battery is the product of the current through the battery and the EMF of the battery.

Similarly, the power dissipated through a resistor is the product of the current through the resistor and the potential across the resistor. Ohm's law allows us to write power in other useful ways.

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