Answer
Verified
377.7k+ views
Hint: The current passing through the electric lamp can be calculated by applying Ohm’s law to it which states that the current passing through the lamp is directly proportional to the voltage applied across it. When an electric lamp is marked as \[60{\text{ W}}\], \[{\text{240 V}}\], it means that the consumes \[60{\text{ J}}\] of energy per unit time when connected to a \[{\text{240 V}}\] power supply.
Formula used:
The power of the electric lamp is associated with the voltage applied to it as
\[P = \dfrac{{{V^2}}}{R}\] …… (1)
Here, \[P\] is the power of the lamp, \[V\] is the voltage applied, and \[R\] is the resistance of the electric bulb.
And, the Ohm's Law is given by
\[V = IR\] …… (2), where \[I\] is the current passing through the circuit.
Complete step by step answer:
In the question, it is given that the power of the electric lamp is \[60{\text{ W}}\] and the marked voltage is \[{\text{240 V}}\]
Substitute \[60{\text{ W}}\] for \[P\], and \[{\text{240 V}}\] for \[V\] in equation (1) as
\[60 = \dfrac{{{{240}^2}}}{R}\]
\[ \Rightarrow R = \dfrac{{240 \times 240}}{{60}}\]
\[ \Rightarrow R = 960{\text{ }}\Omega \]
Substitute \[960{\text{ }}\Omega \] for \[R\], and \[{\text{220 V}}\] for \[V\] in equation (2) as
\[220 = I\left( {960} \right)\]
\[ \Rightarrow I = \dfrac{{220}}{{960}}\]
\[ \Rightarrow I = 0.23{\text{ A}}\]
Therefore, the current passing through the electric lamp is \[0.23{\text{ A}}\].
Now, substitute \[{\text{220 V}}\]for \[V\], and \[960{\text{ }}\Omega \] for \[R\] in equation (1) as
\[P = \dfrac{{{{220}^2}}}{{960}}\]
\[ \Rightarrow P = \dfrac{{48400}}{{960}}\]
\[ \Rightarrow P = 50.42{\text{W}}\]
Also, the power is given defined by work done per unit time and is expressed as
\[P = \dfrac{W}{t}\] …… (3)
Here, \[W\] is the work done and \[t\] is the time.
Substitute \[50.42{\text{ W}}\] for \[P\] and \[1{\text{ hr}}\] for \[t\] in equation (3) as
\[50.42{\text{ W}} = \dfrac{W}{{1{\text{ hr}}}}\]
\[ \Rightarrow W = 50.42{\text{ W}} \times 1{\text{ hr}}\]
\[ \Rightarrow W = 50.42{\text{ W}} \times 3600{\text{ s}}\]
\[ \Rightarrow {\text{W = 181512 J}}\]
Therefore, the electric lamp consumes \[{\text{181512 J}}\] in \[1{\text{ hr}}\].
Note: Power defines the amount of energy that is converted or transferred in an electric circuit per unit of time. It's S.I. The unit is Watt, \[{\text{W}}\], which is equal to one joule of energy consumed in one second.
Formula used:
The power of the electric lamp is associated with the voltage applied to it as
\[P = \dfrac{{{V^2}}}{R}\] …… (1)
Here, \[P\] is the power of the lamp, \[V\] is the voltage applied, and \[R\] is the resistance of the electric bulb.
And, the Ohm's Law is given by
\[V = IR\] …… (2), where \[I\] is the current passing through the circuit.
Complete step by step answer:
In the question, it is given that the power of the electric lamp is \[60{\text{ W}}\] and the marked voltage is \[{\text{240 V}}\]
Substitute \[60{\text{ W}}\] for \[P\], and \[{\text{240 V}}\] for \[V\] in equation (1) as
\[60 = \dfrac{{{{240}^2}}}{R}\]
\[ \Rightarrow R = \dfrac{{240 \times 240}}{{60}}\]
\[ \Rightarrow R = 960{\text{ }}\Omega \]
Substitute \[960{\text{ }}\Omega \] for \[R\], and \[{\text{220 V}}\] for \[V\] in equation (2) as
\[220 = I\left( {960} \right)\]
\[ \Rightarrow I = \dfrac{{220}}{{960}}\]
\[ \Rightarrow I = 0.23{\text{ A}}\]
Therefore, the current passing through the electric lamp is \[0.23{\text{ A}}\].
Now, substitute \[{\text{220 V}}\]for \[V\], and \[960{\text{ }}\Omega \] for \[R\] in equation (1) as
\[P = \dfrac{{{{220}^2}}}{{960}}\]
\[ \Rightarrow P = \dfrac{{48400}}{{960}}\]
\[ \Rightarrow P = 50.42{\text{W}}\]
Also, the power is given defined by work done per unit time and is expressed as
\[P = \dfrac{W}{t}\] …… (3)
Here, \[W\] is the work done and \[t\] is the time.
Substitute \[50.42{\text{ W}}\] for \[P\] and \[1{\text{ hr}}\] for \[t\] in equation (3) as
\[50.42{\text{ W}} = \dfrac{W}{{1{\text{ hr}}}}\]
\[ \Rightarrow W = 50.42{\text{ W}} \times 1{\text{ hr}}\]
\[ \Rightarrow W = 50.42{\text{ W}} \times 3600{\text{ s}}\]
\[ \Rightarrow {\text{W = 181512 J}}\]
Therefore, the electric lamp consumes \[{\text{181512 J}}\] in \[1{\text{ hr}}\].
Note: Power defines the amount of energy that is converted or transferred in an electric circuit per unit of time. It's S.I. The unit is Watt, \[{\text{W}}\], which is equal to one joule of energy consumed in one second.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE