When a resistor carries a current "I" its power dissipation is "P". If the same resistor carries the current of "3 I" the power dissipation will be:

1. Break Down the Problem

We know that the power dissipation $P$ across a resistor can be calculated using the formula: $P = I^2 R$ Where $I$ is the current, and $R$ is the resistance. Given that the current becomes $3I$, we will need to find the new power dissipation $P'$.

2. Relevant Concepts

Using the same formula for power dissipation, we can express the new power $P'$ when the current is $3I$: $P' = (3I)^2 R$

3. Analysis and Detail

Now we calculate $P'$: $P' = (3I)^2 R = 9I^2 R$ Since we know that $P = I^2 R$, we can substitute: $P' = 9P$ Thus, the power dissipation when the current is $3I$ will be 9 times the initial power dissipation.

4. Verify and Summarize

We ensured our calculations were correct by following the principles of electrical power dissipation. The new power dissipation $P'$ when the current is increased to $3I$ indeed results in a value that is nine times the original power $P$.

Final Answer

The power dissipation will be $9P$.