Question

An 80 Ω and a 120 Ω resistor are connected in parallel with a battery. The 120 Ω resistor dissipates energy at a rate of 0.30 W. What is the power dissipated by the 80 Ω resistor?

A. 0.97 W
B. 0.20 W
C. 0.63 W
D. 0.30 W
E. 0.45 W

Answer 1

The power dissipated by the 80 Ω resistor is 0.45 W when the 120 Ω resistor dissipates energy at a rate of 0.30 W in a parallel connection with the same battery.

Step-by-step explanation:

The power dissipated by the 80 Ω resistor can be found by considering that the voltage across both resistors in a parallel connection is the same. Given that the 120 Ω resistor dissipates power at a rate of 0.30 W, we can first calculate the voltage across it. Using the formula for power, P = IV, and Ohm’s law, V = IR, we can combine them into P = I2R or P = V2/R, which allows us to solve for voltage:

V2 = PR

Now we can solve for I (current) for the first resistor, and since the current through both resistors is different, but the voltage is the same due to the parallel connection, we use the voltage found to calculate the power for the 80 Ω resistor:

√(PR) = √(0.30 W × 120 Ω) = 6 V

Now using the voltage for the 80 Ω resistor:

P = V2/R = 6 V2/80 Ω = 0.45 W

So, the correct answer is E. 0.45 W.