Electrical Power

 Electrical Energy and Electrical Power

Work: 

In physics, work is said to be done when a force is applied to an object, causing it to move in the direction of the force. Mathematically, work (W) is defined as the product of the force (F) applied to an object and the displacement (d) of the object in the direction of the force.

W = F x d

In electrical terms, work is done when a charged particle moves through an electric field. When a voltage (electric potential difference) is applied across a circuit, and current flows through it, work is done by the electric field on the charges, enabling the transfer of energy within the circuit. The energy is supplied by the battery.

Recall, Potential Difference or Voltage is mathematically written as follows:

Voltage (V) = Work done (W) / Charge (Q)

Or W = V x Q ------------- (i)

Energy: Energy is the ability to do work.

Electrical energy is the energy related with the movement of charged particles i.e. electrons through a conductor in an electric circuit. It is the ability of an electric current to do work.

From  equation (i), we get -

Electrical Energy (E) = V × Q ------------- (ii)

Power: Power is the rate at which work is done or the rate at which energy is transferred or converted. In electrical systems, power is the rate at which electrical energy is transferred or used.

Mathematically,

Power = Work done or Energy transferred or Converted / Time

P = E / t ------------- (iii)

Using (ii) in (iii), we have

P = V x Q / t

P = V x I {from definition of Current (I) =Q / t} ———- (iv)

The SI unit of electric power is watt (W). It is the power consumed by a device that carries 1 A of current when operated at a potential difference of 1 V. Thus,

1 W = 1 volt × 1 ampere = 1 V A

The unit watt is small; therefore, Kilowatt is used.

Electrical Power = Voltage x Current, the unit is watts (W)

We know

Energy = Power x Time where unit of Energy is Joule, unit of Power is Watt

Ex. If I purchase a bulb of 60 Watt, it means it consumes 60 Joules of Electrical Energy per second.

Energy supplied to the circuit by the source in time t,

E = P x t

= V x I x t {from (iv)}

The unit for electric energy is watt hour (W h). The commercial unit of Electric energy is kilowatt hour (kW h),

1 kW h = 1000 watt × 3600 second

             = 3.6 x 10⁶ Watt-Second

${\mathrm{}}^{}$

             = 3.6 x 10⁶ joule (J)

Solved Numerical:

1.  An electric bulb is connected to a 220 V generator. The current is 0.50 A. What is
     the power of the bulb?

      Given: V = 220 Volt and I = 0.50 A

      We know,

           P = V x I

                = 220 x 0.5

                = 110 J/s or Watt

h   

2.  Two lamps, one rated 100 W at 220 V, and the other 60 W at 220 V, are connected in

     parallel to electric mains supply. What current is drawn from the line if the supply voltage

     is 220 V? Also find the total resistance.

     

     

     Given: P1 = 100 W, P2 = 60 W, V = 220 V

    a)

We know, P = V x I

                 I = P/V

                 I1 = P1/V

                      = 100/220 A

Resistance of Lamp 1

V = I x R

R1 = V/I1

= 220/100/220 ohms

= 220 x 220 /100

            = 484 ohms

Similarly,

b)

I2 = P2/V

     = 60/220 A

R2 = V/I2

     = 220/60/220

     = 220 x 220/60

     = 2420/3 ohms

To find equivalent Resistance, Both Lamps are connected in parallel

1/R = 1/R1 + 1/R2

       = 1 / 484 + 3 / 2420

       = 2420 / 8 ohms

To find Current drawn through mains

I = V / R

  = 220 / (2420 / 8)

  = 220 x 8 /2420 A

  = 0.73 A

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