If the current I through a resistor is increased by 100% (assume that temperature remains unchanged), the increase in power dissipated will be?

To determine the increase in power dissipated when the current through a resistor is increased by 100%, we can follow these steps:

1. Start by understanding the relationship between current, resistance, and power. According to Ohm's Law, the power dissipated in a resistor can be calculated using the formula: P = I^2 * R, where P is the power, I is the current, and R is the resistance.

2. Assume that the initial current through the resistor is represented by I1.

3. Calculate the initial power dissipated using the formula: P1 = I1^2 * R.

4. Since the current is increased by 100%, the new current can be represented as I2 = I1 + (100/100) * I1 = 2 * I1.

5. Calculate the new power dissipated using the formula: P2 = I2^2 * R = (2 * I1)^2 * R = 4 * I1^2 * R.

6. Determine the increase in power dissipated by subtracting the initial power from the new power: Increase in power = P2 - P1 = 4 * I1^2 * R - I1^2 * R = 3 * I1^2 * R.

Therefore, the increase in power dissipated when the current through a resistor is increased by 100% is 3 times the initial power dissipated.