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Draw the circuit using ideal circuit elements: Now, the series current is: $$I = \dfrac{\mathcal{E}}{R_{internal}+ R_{load}}$$ The voltage across the internal resistance is: $$V = \mathcal{E} \dfrac{R_{internal}}{R_{internal}+ R_{load}}$$ The power dissipated by the internal resistance can by found three equivalent ways: P = VI = ...

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Consider your simple example: a car with a fixed power output of $1000 \text{ W}$ accelerating against a constant frictional force of $5\text{ Newtons }$ (Even better, assume that there is no friction, but the car is climbing a very gentle slope, such that gravity exerts $5\text{ Newtons}$ of force back along the slope.) Assume that it has reached a ...

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The expression $P=Fv$ expresses a relation between the instantaneous power, the force and the velocity. You don't have to average for it to be true. In your case, the velocity in constant. This implies that the net force is zero. Hence, the force propelling the car is equal and opposite to the friction force. We can then use the magnitude of the friction ...

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With respect to power loss concept, when we say that the power is dissipated (or lost as you call it) it means that power was dissipated (or spent) as something else which might be useful (as an example power dissipated in a perfect lamp where all power is converted into radiation) or not useful (example is portion of power lost in heating the motor of fan, ...

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