Question

Derive the equation for electric power.

Answer 1

Let a steady current (I) flow through a conductor when a potential difference (V) is applied across its ends for a time interval (t).

By the core definition of potential difference, the work done (W) to move a total charge (Q) across the conductor is expressed as:

W = V × Q

Since electric current is defined as the rate of flow of charge (\(I = \frac{Q}{t}\)), the total charge can be rewritten as:

Q = I × t

Substituting the value of charge into the work equation gives the expression for total electrical energy:

W = V × I × t

Electric power (P) is defined as the rate at which electrical work is done or energy is consumed over time:

P = `"Work Done (W)"/"Time (t)"`

By substituting the expression for work done into this definition, the time term cancels out to yield the final equation for electric power:

P = `(V xx I xx t)/t`

P = V × I