The power, in watts, dissipated as heat in a resistor varies jointly with the resistance, in ohms, and the square of the current, in amperes.A 10-ohm resistor carrying a current of 1 ampere dissipates 10 watts.
How much power is dissipated in a 50-ohm resistor carrying a current of 9 amperes?
A) $P = 50$ Watts
B) $P = 45 \mathrm { Watts }$
C) $P = 9 \mathrm { Watts }$
D) $P = 4,050 \mathrm { Watts }$
E) $P = 5$ Watts

Question

The power, in watts, dissipated as heat in a resistor varies jointly with the resistance, in ohms, and the square of the current, in amperes.A 10-ohm resistor carrying a current of 1 ampere dissipates 10 watts.
How much power is dissipated in a 50-ohm resistor carrying a current of 9 amperes? 
A) $P = 50$ Watts
B) $P = 45 \mathrm { Watts }$
C) $P = 9 \mathrm { Watts }$
D) $P = 4,050 \mathrm { Watts }$
E) $P = 5$ Watts

Quizplus · Accepted Answer

We know that the power, P, varies jointly with the resistance, R, and the square of the current, I:

P = kRI^2

where k is the constant of proportionality. We can solve for k using the information given in the problem:

10 = k * 10 * 1^2
k = 1

Now we can use this value of k to find the power dissipated in the 50-ohm resistor:

P = 1 * 50 * 9^2 = 4,050 Watts.

Therefore, the answer is D.

The Power, in Watts, Dissipated as Heat in a Resistor P=50P = 50P=50

The Power, in Watts, Dissipated as Heat in a Resistor $P = 50$