If the current through a resistor is tripled, what happens to the power dissipat

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Question: If the current through a resistor is tripled, what happens to the power dissipated in the resistor? (2022)

Options:

Correct Answer: Increases by 9 times

Exam Year: 2022

Solution:

Power is proportional to the square of the current (P = I²R). If I is tripled, P increases by 3² = 9 times.

If the current through a resistor is tripled, what happens to the power dissipated in the resistor? (2022)

If the current through a resistor is tripled, what happens to the power dissipated in the resistor? (2022)

Step 1: Understand the formula for power in a resistor, which is P = I²R, where P is power, I is current, and R is resistance.
Step 2: Identify what happens when the current (I) is tripled. If the original current is I, the new current becomes 3I.
Step 3: Substitute the new current into the power formula: P = (3I)²R.
Step 4: Calculate (3I)², which equals 9I².
Step 5: Now the power formula becomes P = 9I²R, which means the new power is 9 times the original power.
Step 6: Conclude that if the current through the resistor is tripled, the power dissipated in the resistor increases by 9 times.

Power and Current Relationship – Understanding that power (P) dissipated in a resistor is proportional to the square of the current (I) flowing through it, as described by the formula P = I²R.