Electrical Power
Category : 10th Class
When electric current flows through the circuit it use up the electrical energy to do certain amount of work. The rate of doing work by the electric current is called the electrical power. It is given by
\[\text{Power }=\frac{\text{Electrical Work Done}}{\text{Time Taken}}\]
Or, \[P=\frac{W}{T}\]
The SI unit of power is watt or joule per second. The power of one watt is defined as the rate of doing work of one joule per second. One kilowatt is equal to the 1000 watt. We can also define the electrical power as the rate of consuming electrical energy.
Since we have, \[P=\frac{W}{T}\]
But work done is equal to the
\[B=V\times I\times T\]
Therefore, \[P=\frac{V\times I\times T}{T}\]
\[\Rightarrow \,\,P=V\times I\]
Where V is potential difference and I is the current flowing through the conductor.
But, \[V=I\times R\]
Putting in the above equation we get,
\[P=I\times R\times I\]
\[\Rightarrow \,P={{I}^{2}}\times R\]
Again, \[I=\frac{V}{R}\]
Therefore, \[P=\frac{{{V}^{2}}}{R}\]
Where R is the resistance of the conductor.
Electrical Energy
Electrical energy is defined as the product of power and time. The unit of electrical energy is kilo watt hour.
\[E=P\times t\]
One kilowatt hour is the amount of electrical energy consumed when an electrical appliance of one watt power is used for one hour.
1 Kilo Watt = 1000 watt
Therefore, 1 kilowatt hour = 1000 x 3600
\[=3.6\times {{10}^{6}}\,\text{joules}\] .
Heating Effect of Electric Current
The heat is produced when an electric current is passed through the wire of high resistance. The resistance in the wire offers resistance to the flow of current. Hence, work must be done by the current to keep itself flowing. If W be the work done by the current I flowing through the conductor for time t and Q be the total charge flow during this time against the potential difference V, then
\[W=Q\times V\]
But, \[Q=I\times t\] and \[V=I\times R\]
Therefore, \[W=I\times t\times I\times R\]
\[\Rightarrow \,W={{I}^{2}}\times t\times R\]
Assuming that all the electrical energy consumed during this work done is converted into heat we have,
Heat produced \[(H)={{I}^{2}}\times t\times R\] Joules
Thus, according to joules law of heating:
There are many application of heating effect of the current.
Some of the Heating Effect of the Current are
Identify the series connection in the given figures
(a)
(b)
(c)
(d)
(e) None of these
Answer: (d)
Calculate the equivalent resistance of the circuit given below:
(a)
(b)
(c)
(d)
(e) None of these
Answer: (b)
Which one of the following is a safety device in the household electric circuit?
(a)
(b)
(c)
(d)
Answer: (a)
Calculate the electrical energy consumed by a electric bulb of 100 watt in 40 hours.
(a) 3 kwh
(b) 2 kwh
(c) 4 kwh
(d) 6 kwh
(e) None of these
Answer (c)
Which one of the following appliances produces the maximum heat when electric current flows through it?
(a)
(b)
(c)
(d)
(e) None of these
Answer: (b)
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