Digital PSAT Math Practice Question 250: Answer and Explanation

Question: 250

The formula for electric power, P, is P = I × V, where I is the current, and V is the voltage. The formula for voltage is V = I × R, where I is also the current, and R is the resistance. How will the power of a given current be affected if the resistance is doubled and the voltage quadrupled?

• A. It will be doubled.
• B. It will be quadrupled.
• C. It will be 8 times greater.
• D. It will be 16 times greater.

Correct Answer: C

Explanation:

(C) First, you need to get the power equation in terms of just resistance and voltage so that you can tell how changing these two quantities will change the power. Therefore, you need to get rid of current by solving for it in the second equation and plugging this expression into the power formula.

Since V = IR, then . Now plug this in for current in the power equation:

. The problem states that resistance is doubled and voltage is quadrupled, so fill these coefficients in:

. Therefore, you can see that power has been multiplied eightfold, choice (C).