Question

When a current is passed in a conductor, 3 \[{}^\circ C\] rise in temperature is observed. If the strength of the current is made thrice, then rise in temperature will be approximately be:
A. 36 \[{}^\circ C\]
B. 27 \[{}^\circ C\]
C. 18 \[{}^\circ C\]
D. 9 \[{}^\circ C\]

Answer 1

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.