Question

Use the diagram to determine total resistance. (Round the FINAL answer to one decimal place.) Note: Use the rated voltage and wattage to determine resistance. Note: Ra and Rb represent the resistance of the wire. The 120 volts of the motor and lamps is their rated voltage and not the actual voltage. I know the answer is 22.7 Ohms. I get very close, but I am not 100%.. I need to be 100%. If you can also: with the same diagram I need the total current as well! Thank you very much.

Answer 1

• 22.6622 Ω ≈ 22.7 Ω
• 5.29516 A ≈ 5.3 A

Step-by-step explanation:

For an electric motor, 1 hp = 746 W, so 1/2 hp = 373 W. Then the total wattage of the load is ...

Pl = 373 +100 +100 +75 = 648 W

The equivalent resistance is ...

R = V^2/P = (120 V)^2/(648 W) = 22 2/9 Ω

Adding the wiring resistance, we get a circuit resistance of ...

22.2222 +0.22 +0.22 = 22.6622 Ω . . . . total circuit resistance

Then the circuit current is ...

120 V/(22.6622 Ω) ≈ 5.29516 A

Circuit resistance is about 22.7 Ω; circuit current is about 5.3 A.

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Exact values are 5099/225 ohms and 27000/5099 amps. Of course, these assume the motor and lamps are purely resistive, which they are not.