Determine the constant of variation for the stated condition.
-The power that a resistor must dissipate is jointly proportional to the square of the current flowing through the resistor and the resistance of the resistor. If a resistor needs to dissipate 28 watts of power when 2 amperes of current is flowing through the resistor whose resistance is 7 ohms, find the power that a resistor needs to dissipate when 3 amperes of current are flowing through a resistor whose resistance is 7 ohms.
A) 63 watts
B) 21 watts
C) 147 watts
D) 42 watts

Question

Quizplus · Accepted Answer

The power dissipated by a resistor, according to the given condition, is directly proportional to the square of the current (I^2) and the resistance (R). The formula for power (P) is P = k*I^2*R, where k is the constant of proportionality. Given P = 28 watts, I = 2 amperes, and R = 7 ohms, we can find k by rearranging the formula: 28 = k*(2^2)*7. Solving for k gives us k = 1. To find the power dissipated with 3 amperes of current and the same resistance, we use P = 1*(3^2)*7 = 63 watts.

Determine the Constant of Variation for the Stated Condition