PX157 - B13c - electromotive force

energy and power in circuits

U = q V

Δ U = q n v_{d} Δ t A V = Δ Q V = I Δ t V

P = \frac{d U}{d t} ≃ \frac{Δ U}{Δ t} = V I

for a resistor, $P = V I = R I^{2} = \frac{V^{2}}{R} > 0$
- takes energy out of a circuit
- power delivered by the battery is dissipated in the circuit, ohmic heating:

P = R I^{2}

\frac{P}{V o l .} = \frac{ρ L}{A} \frac{J^{2} A^{2}}{V o l .} = ρ J^{2}

$\vec{E}$ inside the battery acts opposite to $\vec{E}$ in the circuit
requirements to maintain a steady current:
- closed circuit
- source of energy to move charges against the electric field in the battery, which is provided by a force such that:

\vec{F} = - q \vec{E}