Physics - Electricity and Magnetism

A ceiling fan operates at three speeds, using 120 V of electricity from the wall. At low speeds, it uses 0.25 A. Calculate the resistance needed to generate that current. Then in 1-2 sentences, describe how the resistance would change at medium and high speeds if larger currents are needed at those speeds. Your answer should include the calculated resistance and a sentence describing your reasoning.

II. Since current is inversely proportional to the resistance in the electrical circuit, an increase in the current (larger currents) flowing into the electrical circuit of the ceiling fan would cause the resistance to decrease in magnitude at medium and high speeds.

Given the following data:

Voltage = 120 Volts

Current = 0.25 Ampere

To calculate the resistance needed to generate that current, we would apply Ohm's law:

Ohm's law states that at constant temperature, the current flowing through an electrical circuit is directly proportional to the voltage (potential difference) applied across the two terminals of the electrical circuit and inversely proportional to the resistance in the electrical circuit.

Mathematically, Ohm's law is given by the formula;

[tex]V=IR[/tex]

Where;

V is the voltage measured in Volts.

I is the current measured in Ampere.

R is the resistance measured in Ohms.

Making R the subject of formula, we have:

[tex]R =\frac{V}{I}[/tex]

Substituting the given parameters into the formula, we have;

[tex]R=\frac{120}{0.25}[/tex]

Resistance, R = 480 Ohms

Since current is inversely proportional to the resistance in the electrical circuit, an increase in the current (larger currents) flowing into the electrical circuit of the ceiling fan would cause the resistance to decrease in magnitude at medium and high speeds.

In conclusion, the larger the current, the lower the resistance would be at both medium and high speeds.

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