When the current through a resistor is increased by a factor of 4, how does the power dissipated by the resistor change?

• A. The power increases by a factor of 8.
• B. The power increases by a factor of 16.
• C. The power increases by a factor of 4.
• D. The power remains the same.

Answer: (B)

Verified step by step guidance

1. Start by recalling the formula for power dissipated in a resistor: \( P = I^2 R \), where \( P \) is the power, \( I \) is the current, and \( R \) is the resistance.
2. Understand that the resistance \( R \) remains constant in this scenario, as the problem does not indicate any change in resistance.
3. Consider the change in current: the current \( I \) is increased by a factor of 4. This means the new current \( I' = 4I \).
4. Substitute the new current into the power formula: \( P' = (4I)^2 R = 16I^2 R \).
5. Compare the new power \( P' \) with the original power \( P = I^2 R \). The new power is \( 16 \) times the original power, indicating that the power increases by a factor of 16.