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, we need to understand the relationship between power, current, voltage, and resistance.
The formula for power in a circuit is given by:
P = I^2 * R
where P is power, I is the current flowing through the resistor, and R is the resistance.
Now, let's analyze the options to see which one will result in doubling the power.
a. Doubling the current while doubling the resistance:
If we double the current (I) and double the resistance (R), the power equation becomes:
P' = (2I)^2 * (2R) = 4(I^2) * 2R = 8(I^2 * R)
So, the power will be multiplied by a factor of 8, not doubled. Therefore, option a is incorrect.
b. Doubling the current by making a resistance half as big:
If we double the current (I) by making the resistance (R) half as big, the power equation becomes:
P' = (2I)^2 * (0.5R) = 4(I^2) * 0.5R = 2(I^2 * R)
In this case, the power will be doubled, as the expression 2(I^2 * R) is twice the original power. Therefore, option b is correct.
c. Doubling the current by doubling the voltage:
If we double the current (I) by doubling the voltage (V), the power equation becomes:
P' = (2I)^2 * R = 4(I^2) * R = 4(I^2 * R)
In this case, the power will be multiplied by a factor of 4, not doubled. Therefore, option c is incorrect.
d. Doubling the current while making the voltage half as big:
If we double the current (I) while making the voltage (V) half as big, the power equation becomes:
P' = (2I)^2 * (0.5V) = 4(I^2) * 0.5V = 2(I^2 * V)
In this case, the power will be doubled, as the expression 2(I^2 * V) is twice the original power. Therefore, option d is also correct.
Therefore, both options b and d will double the power given off by a resistor.