Work and Power In A Circuit

Inside wires, there are flowing charges, electrons or positive “holes”, which are known as current. Due to the fact these charges are moving through the wires, it can be inferred that there is some kind of force acting on them and doing work as the particle traverses the wire. This work and subsequently power can be calculated.

Short Description of Topic

The Main Idea

Mechanical work is the product of force and displacement. Electrical work can be related to this by considering a particle with charge “q” in a region or electrical field “E”. The force acting on that particle would be F = q*E. As the force begins to act on the particle, the particle will begin to move. As the particle moves the work on that product is the integral of E dot multiplied with the displacement of the charged particle. Alternatively, the Force can be calculated by determining the potential difference and multiplying by the charge “q”. Inside a wire, the same principals apply. The Pockets or charge, whether they are positive “holes” or electrons, that are moving through wires because of a force generated by an electric field.

A Mathematical Model

As the charged particles in the wire move, the electric potential of that particle decreases. This change in electric potential (dV) can be used to calculate the change in electric potential energy (dU).

dU = (dq)(dV) -Work = dU

Power is equal to the work done over the change in time.

Power = | dU/ dt | = | (dq*dV)/dt |

However, current “I” is equal to dq/dt so…

Power = | I(dV) |

A Computational Model

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