Understanding Circuit Resistance: A Practical Homework Problem

Homework can often feel like a daunting task, especially when it involves topics like circuit resistance and appliances. However, reviewing your notes and applying basic principles can make it much easier to tackle. Let's break down the problem and solve it step by step.

Problem Setup

Consider a 220-volt circuit that has the following appliances turned on:

Air conditioner: 1500 watts Water motor: 100 watts Flat iron: 1000 watts

Determine the Resistance of Each Appliance

To find the resistance of each appliance, we will use the power equation in combination with Ohm's law. The power equation is:

Watts Volts x Amps

We can rearrange this to find the current:

Amps Watts / Volts

Knowing the current, we can then use Ohm's law to find the resistance:

Resistances Volts / Amps

Air Conditioner

Watts: 1500 Volts: 220

Amps 1500 / 220 6.82 A

Resistance 220 / 6.82 32.37 Ω

Water Motor

Watts: 100 Volts: 220

Amps 100 / 220 0.45 A

Resistance 220 / 0.45 488.89 Ω

Flat Iron

Watts: 1000 Volts: 220

Amps 1000 / 220 4.55 A

Resistance 220 / 4.55 48.32 Ω

Equivalent Resistance in Parallel

Now, we need to find the equivalent resistance if all the appliances are in parallel. The formula for resistors in parallel is:

1/Equivalent Resistance 1/R1 1/R2 1/R3

Substituting the values we found:

1/Equivalent Resistance 1/32.37 1/488.89 1/48.32

1/Equivalent Resistance 0.03087 0.002047 0.020679 0.053596

Equivalent Resistance 1 / 0.053596 18.66 Ω

Quick Check

A quick check of the answer is essential. If each appliance is part of a parallel circuit, the equivalent resistance should be less than the resistance of the item with the lowest resistance.

The lowest resistance is the flat iron, which is 48.32 Ω. The calculated equivalent resistance (18.66 Ω) is indeed much lower than 48.32 Ω, confirming our calculations are correct.

Conclusion

Circuit resistance can seem complex, but breaking it down into steps and using the fundamental principles of electricity makes it manageable. By understanding how to calculate individual resistances and how to find the equivalent resistance in a parallel circuit, you can solve similar homework problems confidently.

Remember, the goal is not just to complete the homework but to grasp the concepts and apply them in different scenarios. If you need further help, don't hesitate to review your notes or consult additional resources.