16.3 – Electrical Energy | Physics with Mr Shone

Electrical Energy

Electrical energy can be determined by:

$E = Pt$

Where:

$E$ = the electrical energy: joules (J)
$P$ = electrical power: watts (W)
$t$ = time: seconds (s)

As we know $P = I V$ we can say:

$E = V I t$

Where:

$E$ = total electrical energy: joules (J)
$V$ = potential difference across component: volts (V)
$I$ = current flowing through component: amperes (A)
$t$ = time: seconds (s)

Example: Finding Energy in Joules
What is the energy used by a 2.0 V bulb in one minute, if a current of 0.5 A flows though it? $E = V I t$ $E$ = 2.0 × 0.5 × 60 $E$ = 60 J

The kilowatt-hour

Although the SI unit of electrical energy is Joule (J), another common unit for electrical energy usage is the kilowatt-hour (kWh). We still use the same equation but with a different set of units.

$E = Pt$

Where:

$E$ = the electrical energy: kiolwatt-hour (kWh)
$P$ = electrical power: kilowatts (kW)
$t$ = time: seconds: hour (h)

Example: Finding Energy in Kilowatt-hours (kWh)
What is the energy used by a 1500 W air-conditioner in running for 8 hours? $E$ = $P$ × $t$ $E$ = 1.5 × 8 $E$ = 12 kWh

Example 2
How long will a 60 W laptop run on 0.36 kWh of electrical energy? $P$ = 60 W = 0.060 kW $E$ = $P$ × $t$ $t$ = $E$ / $P$ $t$ = 0.36 kWh / (0.060 kW) $t$ = 6.0 hours

Joules vs Kilowatt-Hours
Consider a 1000 W appliance switched on for one hour. Power used (in joules) is: $E$ = $P$ × $t$ $E$ = 1000 × (1 × 60 × 60) $E$ = 3 600 000 J Power used (in kWh) is: $E$ = $P$ × $t$ $E$ = 1 × 1 $E$ = 1 kWh Thus, 1 kWh = 3,600,000 J (3.6 MJ)

Joules vs Kilowatt-Hours

Consider a 1000 W appliance switched on for one hour.

Power used (in joules) is:

$E$ = $P$ × $t$

$E$ = 1000 × (1 × 60 × 60)

$E$ = 3 600 000 J

Power used (in kWh) is:

$E$ = $P$ × $t$

$E$ = 1 × 1

$E$ = 1 kWh

Thus,

1 kWh = 3,600,000 J (3.6 MJ)

Electricity meter is the instrument used by the electricity company to measure the amount of electrical energy consumed.

Reading an Electricity Meter
meter showing 60836.3 kWh of electrical energy having been used Older meters had dials in which each pointer should be read to the lower number. meter showing 8542 kWh of electrical energy having been used

Reading an Electricity Meter

meter showing 60836.3 kWh of electrical energy having been used

Older meters had dials in which each pointer should be read to the lower number.

meter showing 8542 kWh of electrical energy having been used

1 kWh of energy is sometimes referred to as a unit of electrical energy.

Cost of electricity consumed = Electrical energy usage measured in kilowatt-hour (kWh) x cost per kWh

Cost of electricity consumed = No. of Units x cost per Unit

Example (Cost of Electricity)
How much does it cost to run a 100 W fridge for 30 days if electricity is sold at $0.25 per kWh? $E$ = $P$ × $t$ $E$ = 0.100 × 30 × 24 $E$ = 72 kWh Cost = number of kWh × Cost per kWh = 72 x 0.25 = 18.00 dollars

Example 3
How much will it cost to use a 2500 W air-conditioner for a week if electricity cost 30.0¢ per unit and it is switched on for 6 hours a day? $E$ = $P$ × $t$ $E$ = 2.50 kW × 6 hr × 7 days $E$ = 105 kWh Cost = number of kWh × Cost per kWh = 105 kWh x 30.0 ¢/kWh = 3150 ¢ = 31.50 dollars

Caution: A Common Mistake
Be careful with pricing – don’t mix up dollars and cents.

Electrical Energy

The kilowatt-hour

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