The amount of electric that is consumed by an electric energy can be easily calculated and the cost of electric energy used for a particular appliance can also be calculated

 

 

 

Electrical energy Equations

The amount of electric energy transferred to an appliance depends on its power and the length of time it is switched on. The amount of mains electric energy transferred is measured in kilowatt-hours, kWh. One unit is 1 kWh.

E = P × t

  • E is the energy transferred in kilowatt-hours, kWh

  • P is the power in kilowatts, kW

  • T is the time in hours, h.

Note that power is measured in kilowatts here instead of the more usual watts. To convert from W to kW you must divide by 1,000.

For example, 1,000 W = 1,000 ÷ 1,000 = 1 kW.

Also note that time is measured in hours here, instead of the more usual seconds. To convert from seconds to hours you must divide by 3,600.

For example, 7,200 s = 7,200 ÷ 3,600 = 2 h.

 

 

Ohm’s Law

The most important description of electric energy is ohm’s law. It states that

“At constant temperature, the current through the conductor is directly proportional to the potential difference across the points”

i.e.  V α I

And it can also be written as V=IR

Where R is the resistance of the conductor

 

Formula for calculating power from electric energy

The formula that links energy and power is:

Energy = Power x Time.

The unit of energy is the joule, the unit of power is the watt, and the unit of time is the second.

If we know the power in watts of an appliance and how many seconds it is used we can calculate the number of joules of electric energy which have been converted to sortie other form.

 E.g. If a 40 watt lamp is turned on for one hour, how many joules of electric energy have been converted by the lamp?

Energy (w) = Power x Time

Energy = 40 x 3600

= 14,400 joules

 

Examples of electric energy

Calculate the heat produced by an electric iron, which has a resistance of 30 ohms and takes a current  of  3 amperes when it is switched on for 15 seconds.

Energy = Power x Time

Power = I2R

 =32 * 30

  = 270 watts

Energy = Power x Time

 = 270 x 15

= 4050 joules

Important facts regarding electric energy equations

  • We pay for energy (not charge or current or voltage).

  • The electricity companies use a non-SI unit, the kWh, to calculate our bills.

 

Points to remember

The electric energy is defined as the total work done or energy supplied by the source of e.m.f. in maintaining the current in an electric circuit for a given time:
              Electric energy = electric power × time = P × t.

Thus the formula for electric energy is given by:
               Electric energy = P × t = V × I × t = I2 × R × t = V2t / R.

 

  • S.I unit of electric energy is joule (denoted by J), where 1joule = 1watt × 1 second = 1volt × 1ampere × 1second.

  • Commercial unit of electric energy is kilowatt-hour (kWh), where 1kWh = 1000 Wh = 3.6 ×106J = one unit of electric energy consumed.

  • The number of units of electric energy consumed is n = (total wattage × time in hour)/1000.

  • The cost of consumption of electric energy in a house = no. of units of electric energy consumed × amount for one unit of electric energy.

 

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