Which process will double the power given off by a resistor?

a. Doubling the current while doubling the resistance

b. Doubling the current by making a resistance half as big

c. Doubling the current by doubling the voltage

d. Doubling the current while making the voltage half as big

i think the answer is B but i don't know how to get there

To determine which process will double the power given off by a resistor, you need to understand the relationship between power, current, and resistance.

The power (P) dissipated by a resistor can be calculated using the formula P = I^2 * R, where I is the current flowing through the resistor and R is the resistance of the resistor.

Now, let's analyze each option:

a. Doubling the current while doubling the resistance.
If you double both the current (I) and the resistance (R), the power would be 2I * 2R = 4IR. This process does not result in doubling the power, so option a can be eliminated.

b. Doubling the current by making a resistance half as big.
If you double the current (I) and halve the resistance (R), the power would be 2I * (1/2)R = I * R. This process results in doubling the power, as the power is proportional to the product of current and resistance. Therefore, option b is correct.

c. Doubling the current by doubling the voltage.
If you double the current (I) and double the voltage (V), the power would be 2I * 2V = 4IV. This process does not result in doubling the power, so option c can be eliminated.

d. Doubling the current while making the voltage half as big.
If you double the current (I) and halve the voltage (V), the power would be 2I * (1/2)V = IV. This process does not result in doubling the power, so option d can be eliminated.

Therefore, the correct answer is b. Doubling the current by making a resistance half as big.