Multiple-Concept Example 9 discusses the physics principles used in this problem. Three resistors, 2.2, 3.9, and 6.4 Ω, are connected in series across a 24-V battery. Find the power delivered to each resistor.

resistance (Ω) power (W)
2.2 ______
3.9 ______
6.4 ______

To find the power delivered to each resistor, we can use the formula:

Power (P) = (Voltage (V))^2 / Resistance (R)

We are given the resistance values of the three resistors as 2.2 Ω, 3.9 Ω, and 6.4 Ω, and the voltage across the circuit as 24 V.

To find the power delivered to the first resistor (2.2 Ω), we substitute the values into the formula:

Power = (24 V)^2 / 2.2 Ω

Calculating this equation gives us:

Power = 62.18 W

Therefore, the power delivered to the first resistor is 62.18 W.

Next, we can find the power delivered to the second resistor (3.9 Ω) by substituting the values into the formula:

Power = (24 V)^2 / 3.9 Ω

Calculating this equation gives us:

Power = 146.77 W

Therefore, the power delivered to the second resistor is 146.77 W.

Finally, we can find the power delivered to the third resistor (6.4 Ω) by substituting the values into the formula:

Power = (24 V)^2 / 6.4 Ω

Calculating this equation gives us:

Power = 90 W

Therefore, the power delivered to the third resistor is 90 W.

The power delivered to each resistor is as follows:

Resistance (Ω) Power (W)
2.2 62.18
3.9 146.77
6.4 90