Electrical Energy

 

Electrical Energy :- When an electric current is passed through a conductor by a battery, the chemical energy stored inside the battery is converted into the kinetic energy of free electrons in the conductor. Due to continuous collision of free electrons with atoms in the conductor, the kinetic energy of the electrons keeps on getting lost and due to which the temperature of the conductor increases. Therefore, the chemical energy of the battery keeps getting converted into thermal energy of the conductor.

Electrical Energy Definition

 Electrical energy is a form of energy that results from the movement of electric charge, typically in the form of electrons.

Formula of Electrical Energy

An electric battery has two terminals – a negative and a positive terminal. The negative terminal has an excess of electrons while the positive terminal has a deficit of electrons. In the following figure we have connected a resistance R between the terminals of a battery :-

End a of resistance R is connected to the positive end of the battery and end b is connected to the negative end of the battery. The electric potential of a is V(a) and the electric potential of b is V(b). Electric current I flows from end a to b, hence V(a) > V(b). Let the potential difference between a and b be, V(a) – V(b) = V.

Charge flowing through resistance R in time t

Q = It

Change in potential energy of Q

ΔU = Q[V (b)] – Q[V(a)]

⇒ ΔU = Q[V (b) – V(a)]

⇒ ΔU = Q(-V)

⇒ ΔU = – VQ

From the law of conservation of mechanical energy,

Change in kinetic energy(ΔK) + Change in potential energy(ΔU) = 0

ΔK + ΔU = 0

⇒  ΔK = – ΔU

⇒  ΔK  = – (– VQ)

⇒ ΔK = VQ = VIt > 0

Therefore, if the charge will move freely under the influence of electric field, then the kinetic energy of the charge will increase. This kinetic energy of the charge is the main electrical energy (E) used by the battery, hence

E = VIt

According to Ohm’s law V = IR, hence

E = I²Rt

Similarly I = V/R, hence

E = (V²t)/R

When charges collide, the energy they gain is distributed between the atoms. As a result, the vibration of the atoms increases resulting in heating of the conductor. Thus, in a real conductor some amount of energy is dissipated as heat.

Therefore

ΔK = Heat (ΔH)

Or

ΔH = VIt = I²Rt = (V²t)/R

⇒ (ΔH/t) = VI

Hence electric power,

P = VI = I²R = V²/R