Answer
Verified
440.1k+ views
Hint: Heat is generated when electricity flows through the conductor due to the conductor’s resistance. This generated heat gives rise to temperature. The rise in temperature is directly proportional to the heat generated. And the amount of heat generated can be calculated by the formula given.
Formula Used:
\[H={{I}^{2}}R\]
Complete answer:
When current is passed through a conductor there is a movement of the electrons. That movement of electrons encounters resistance. Due to this resistance some energy is lost as heat. This dissipating heat gives rise to the temperature.
When the conductor remains constant, the heat dissipates or the rise in temperature depends upon the Current passing through the conductor. This relation is formulated as.
\[H={{I}^{2}}R\]
Coming to the question, let the heat generated in the first case be \[{{H}_{1}}\],then
\[{{H}_{1}}={{({{I}_{1}})}^{2}}R\]
Where \[{{I}_{1}}\] is the current passing through the conductor in the first case
In the second case the heat generated would be
\[{{H}_{2}}={{({{I}_{2}})}^{2}}R\]
It is also given the final current is thrice the initial current
\[{{I}_{2}}=3{{I}_{1}}\]
So,
\[\begin{align}
& {{H}_{2}}={{(3{{I}_{1}})}^{2}}R \\
& \Rightarrow {{H}_{2}}=9{{({{I}_{1}})}^{2}}R \\
& \Rightarrow {{H}_{2}}=9{{H}_{1}} \\
\end{align}\]
Hence, \[{{H}_{2}}=9{{H}_{1}}\]
We also know that the rise in temperature is directly proportional to the heat generated, when the conductor is the same. Therefore
\[\begin{align}
& H\propto \Delta T~ \\
& \Rightarrow ~\Delta T2=27{{~}^{o}}C \\
\end{align}\]
If the strength of the current is made thrice, then rise in temperature will approximately be 27\[{}^\circ C\]
So, Option B is correct .
Note:
The process by which the passage of an electric current through a conductor produces heat is called Joule heating, also known as resistive, resistance, or Ohmic heating. The rise in temperature observed depends on the current, resistance as well as physical properties of the conductor like specific heat and mass.
Formula Used:
\[H={{I}^{2}}R\]
Complete answer:
When current is passed through a conductor there is a movement of the electrons. That movement of electrons encounters resistance. Due to this resistance some energy is lost as heat. This dissipating heat gives rise to the temperature.
When the conductor remains constant, the heat dissipates or the rise in temperature depends upon the Current passing through the conductor. This relation is formulated as.
\[H={{I}^{2}}R\]
Coming to the question, let the heat generated in the first case be \[{{H}_{1}}\],then
\[{{H}_{1}}={{({{I}_{1}})}^{2}}R\]
Where \[{{I}_{1}}\] is the current passing through the conductor in the first case
In the second case the heat generated would be
\[{{H}_{2}}={{({{I}_{2}})}^{2}}R\]
It is also given the final current is thrice the initial current
\[{{I}_{2}}=3{{I}_{1}}\]
So,
\[\begin{align}
& {{H}_{2}}={{(3{{I}_{1}})}^{2}}R \\
& \Rightarrow {{H}_{2}}=9{{({{I}_{1}})}^{2}}R \\
& \Rightarrow {{H}_{2}}=9{{H}_{1}} \\
\end{align}\]
Hence, \[{{H}_{2}}=9{{H}_{1}}\]
We also know that the rise in temperature is directly proportional to the heat generated, when the conductor is the same. Therefore
\[\begin{align}
& H\propto \Delta T~ \\
& \Rightarrow ~\Delta T2=27{{~}^{o}}C \\
\end{align}\]
If the strength of the current is made thrice, then rise in temperature will approximately be 27\[{}^\circ C\]
So, Option B is correct .
Note:
The process by which the passage of an electric current through a conductor produces heat is called Joule heating, also known as resistive, resistance, or Ohmic heating. The rise in temperature observed depends on the current, resistance as well as physical properties of the conductor like specific heat and mass.
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
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
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