Question

An electric bulb of resistance \[200\Omega \] draws a current of \[1A\] . Calculate the power of the bulb, the potential difference at its ends and the energy in kWh consumed burning it for \[5h\] .

Answer 1

Hint: We are asked to find the energy in kilowatt hour for burning a particular bulb for five hours. We start by noting down all the data given in question. Then we note down the formula to find the power with respect to resistance and current. We can find the value of energy from power as power is the energy done per unit time. The product of power and time gives us energy.

Formulas used:
The formula used to find the power used up by the bulb is given by,
\[P = {I^2}R\]
The formula used to find the energy from power is given by,
\[E = Pt\]
Where \[I\] is the current drawn by the bulb, \[R\] is the electrical resistance provided by the bulb and \[t\] is the time taken by the bulb to draw the given power

Complete step by step answer:
Let us start by noting down the data given in the question,
The resistance offered by the bulb is given as \[R = 200\Omega \]
The current drawn by the given bulb is given as \[I = 1A\]
The time taken to find the energy and power is given as \[t = 5h\]
The power drawn by the given bulb can be found by using the formula, \[P = {I^2}R\]
\[P = {I^2}R = {1^2} \times 200 = 200W\]
Now that we have the power used, we can find the value of energy consumed by the bulb by using the formula, \[E = Pt\]
\[E = Pt \\
\Rightarrow E = 200 \times 5 \\
\therefore E = 1000\,Wh\]
We can convert this to the unit asked in our question by dividing it by thousand and get \[1kWh\].

Therefore, the power of the bulb is \[200\,W\] and the energy it consumes in \[5\,h\] is \[1\,kWh\].

Note: The conversion of watt to kilowatt by dividing with a thousand before or after finding the value of energy as it doesn’t affect the unit of time. Power can also be found by dividing the voltage and current (you can also use this relation to get back to the relationship we have used here)