PSAT Math Multiple-Choice Question 790: Answer and Explanation

Question: 790

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 is quadrupled?

• A. The power will be doubled.
• B. The power will be quadrupled.
• C. The power will be 8 times greater.
• D. The power 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, we 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 in these coefficients:

Therefore, you can see that power has been multiplied 8 times, which is choice (C).