A `2^(@)C` rise in temperature is observed in a conductor passing a current. When the current is tripled. The rise in temperature will be

Explanation

To solve the problem, we need to understand the relationship between the current flowing through a conductor and the resulting temperature rise in that conductor. The heat generated in a conductor due to the current can be expressed using the formula:

\[ H = I^2 R t \]

Where:
- \( H \) is the heat generated,
- \( I \) is the current,
- \( R \) is the resistance of the conductor, and
- \( t \) is the time for which the current flows.

The rise in temperature (\( \Delta T \)) of the conductor can also be expressed in terms of the heat generated:

\[ H = mc \Delta T \]

Where:
- \( m \) is the mass of the conductor,
- \( c \) is the specific heat capacity of the material, and
- \( \Delta T \) is the change in temperature.

From the above two equations, we can derive that:

\[ I^2 R t = mc \Delta T \]

This implies that the temperature rise (\( \Delta T \)) is proportional to the square of the current (\( I^2 \)):

\[ \Delta T \propto I^2 \]

### Step-by-Step Solution:

1. **Initial Condition**: We know that a rise in temperature of \( 2^\circ C \) occurs at some initial current \( I \).
\[ \Delta T_1 = 2^\circ C \]

2. **Current Tripled**: When the current is tripled, the new current \( I' \) becomes:
\[ I' = 3I \]

3. **Calculate New Temperature Rise**: Since the temperature rise is proportional to the square of the current, we can express the new temperature rise \( \Delta T_2 \) as:
\[ \Delta T_2 \propto (I')^2 = (3I)^2 = 9I^2 \]

4. **Relate New Temperature Rise to Initial**: We can relate the new temperature rise to the initial temperature rise:
\[ \Delta T_2 = 9 \cdot \Delta T_1 \]

5. **Substituting the Value**: Now substituting the value of \( \Delta T_1 \):
\[ \Delta T_2 = 9 \cdot 2^\circ C = 18^\circ C \]

### Final Answer:
The rise in temperature when the current is tripled will be \( 18^\circ C \).

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