What do you understand by electric energy ? Derive an expression for electric energy.

Explanation

Electric energy: The total amount of work done by the current in an electric circuit is known as electric energy.
Expression for electric energy : Let a conductor is connected with a battery of e.mf V.

Let `V =` potential difference across the ends of the conductor
`I =` current flowing through the conductor
`t =` time for which the current flowing through the conductor
`Q=` charge flowing through the conductor during time `t`
Now, current `I = ("Charge")/("time") = ( Q)/( t)`
`rArr Q = It " "......(i)`
If W is the work done in carrying a charge Q from one end to the other end of the conductor, then
Potential difference, `V = ( W)/( Q) rArr W = VQ`
Or `W = V ( It) = V It" "..........(ii)" "["using equation" (i) ] `
According to Ohm.s law
`V =IR`
Substitute V in equation (ii),
We get
`therefore W = (IR) It = I^(2) Rt`.
Also `W = ((V)/( R))^2 Rt " "[because I = (V)/( R) ]`
`rArr W = ( V^2)/( R) t therefore W = VIt = I^(2) Rt = (V^2)/(R) t`
This work done by the current measures the electric energy,
Therefore, `E = V "It" = I^(2) R t = (V^2)/( R) t`