Power of a circuit
I was wondering how to actually derive the formula for the power of a circuit.
I imagine you would need to start with Energy (U) as a function of the charge and Potential difference. However, I am having trouble on how to actually set the equation up. Is this even on the right track?
Answer
Power is the work done per unit time. In the case of a circuit, the electric power has to do with the charge carriers being forced to move across a potential difference. Imagine charge ΔQ moving across a potential difference V. You know that the potential energy difference is U = VΔQ, so the power is P = VΔQ/Δt. Written as a derivative we notice that the power can be written in terms of the current instead of charge.
P = V dQ/dt = VI
This is the basic formula for electric power. Whenever you have current flowing through a voltage difference, it took energy to make that happen. The power is the product of the current and the voltage.
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Power is the work done per unit time. In the case of a circuit, the electric power has to do with the charge carriers being forced to move across a potential difference. Imagine charge ΔQ moving across a potential difference V. You know that the potential energy difference is U = VΔQ, so the power is P = VΔQ/Δt. Written as a derivative we notice that the power can be written in terms of the current instead of charge.
P = V dQ/dt = VI
This is the basic formula for electric power. Whenever you have current flowing through a voltage difference, it took energy to make that happen. The power is the product of the current and the voltage.