Question

If 1 unit of electricity costs $0.20$ , how much does it cost to switch on a heater marked 120V, 3A for 90 minutes ?
A) 0.11
B) 2.70
C) 64.80
D) 180.00

Answer 1

Hint: The cost of an electronic Appliance depends on the amount of energy used by it. The commercial unit of energy is kWh. Thus the cost to switch on the heater can be calculated if we know the value of energy used by it in commercial units, which is kWh. Then we can find the cost by multiplying the cost of 1 electricity unit and the total kWh of energy consumed.

Formula used:
$Energy = Power \times Time$
$Power = Voltage \times Current$

Complete step by step solution:
Let V be the voltage across the heater
Voltage across the heater $V = 120$ volts
Converting it into kilovolts (therefore dividing it by 1000, as $1kV = 1000$ volts)
Thus, $V=0.12kV$
Let I be the current in the heater
Current flowing through the heater $I = 3A$
Formula for power of the heater is given by $P = VI$
By substituting the values, we get the value of power of the heater,
\[\therefore \;P = 0.12 \times 3 = 0.36\;kW\]
 Let T be the time for which heater is used
Time of usage $(T) = 90{\text{ minutes}}$
Converting it into hours (therefore dividing it by $60$ , as \[1hr = 60mins\] )
Thus time of usage of heater\[ = 1.5{\text{ }}hrs\]
Thus energy consumed is given by $E = PT$
Substituting values,
\[E = 0.36 \times 1.5 = 0.54\;kWh\]
Now the total electricity units consumed by the heater are \[0.54\] kWh.
And cost of 1 unit of electricity \[ = 0.20\]
Cost to switch on heater for 90 minutes \[ = {\text{ }}\;0.54 \times 0.2\] \[ = 0.11\]

Hence, the right answer is (A) that is \[0.11\]

Note: The cost of using any electronic appliance can also be found by using a shortcut formula, that is
Cost \[ = {\text{ }}\dfrac{{\left( {V \times I \times T \times C} \right)}}{{1000}}\] where $V$ voltage in volts, $I$ is current in ampere, $T$ is time in hours and $C$ is cost of one electricity unit.