Ohm's Law

Write down the formula for Ohm's law and state what quantity each letter represents, specifying the unit in which each is measured.

A current of $2\ \text{A}$ flows through a resistor of $5\ \Omega$. What is the voltage across its ends?

A light bulb of $6\ \Omega$ is connected to a $12\ \text{V}$ battery. What current passes through it?

When connecting the motor of a toy boat to a $9\ \text{V}$ battery, a current of $3\ \text{A}$ passes through it. What is the resistance of the motor?

A light bulb of $300\ \Omega$ is connected to a $9\ \text{V}$ battery. Calculate the current passing through it and express the result in amperes and in milliamperes.

A current of $300\ \text{mA}$ flows through the buzzer of a doorbell connected to $4.5\ \text{V}$.

1. a) Express this current in amperes.
2. b) Calculate the resistance of the buzzer.

A circuit has a $6\ \text{V}$ battery and a resistor of $3\ \Omega$.

1. a) Calculate the current that flows.
2. b) If we replace the resistor with one of $6\ \Omega$, what is the current now?
3. c) Explain what happens to the current when the resistance is doubled while keeping the same battery.

A certain current flows when a $5\ \text{V}$ battery is connected to a resistor of $10\ \Omega$.

1. a) Calculate it.
2. b) What current would flow with a $10\ \text{V}$ battery and the same resistance?
3. c) How does the current change when the voltage is doubled? Relate this to Ohm's law.

Andrea says: "If we double the voltage, the current also doubles." Bruno replies: "No, it is halved."

1. a) Who is right if the resistance does not change?
2. b) Verify it by calculating the current passing through a resistor of $8\ \Omega$ with $8\ \text{V}$ and with $16\ \text{V}$.
3. c) Write a sentence summarizing the relationship between voltage and current according to Ohm's law.

We measure the current passing through a resistor by applying different voltages, as shown in the graph: with $2\ \text{V}$, $0.5\ \text{A}$ flows; with $4\ \text{V}$, $1\ \text{A}$; and with $6\ \text{V}$, $1.5\ \text{A}$.

1. a) Calculate the value of the resistance in each measurement.
2. b) What do you conclude?
3. c) Predict the current we will measure if we apply $12\ \text{V}$.

In an experiment with a filament light bulb, you obtain the following results, as shown in the graph: with $2\ \text{V}$, $0.5\ \text{A}$ flows; with $4\ \text{V}$, $0.8\ \text{A}$; and with $6\ \text{V}$, $1\ \text{A}$.

1. a) Calculate the apparent resistance of the light bulb in each case.
2. b) Does the light bulb obey Ohm's law, that is, does it keep its resistance constant?
3. c) Knowing that the filament glows red-hot when lit, propose an explanation for what was observed.

The wire of a scale model melts if more than $2\ \text{A}$ flows through it, and we power it with a $12\ \text{V}$ battery.

1. a) What is the minimum resistance the circuit must have so that the wire does not melt?
2. b) What happens if we use a resistor of $4\ \Omega$? Justify your answer with calculations.

A toy LED can take a maximum of $0.02\ \text{A}$; if more current passes through it, it burns out. We connect it to a $9\ \text{V}$ battery with a protective resistor in the same path, as shown in the figure.

1. a) What is the minimum value this resistor must have?
2. b) What would happen if we connected the LED directly to the battery without a resistor? Explain using Ohm's law.

An unknown resistor is connected to a $24\ \text{V}$ battery, and the ammeter reads $1.5\ \text{A}$, as shown in the figure.

1. a) Calculate the value of the resistance.
2. b) What would the ammeter read if we changed to a $8\ \text{V}$ battery?
3. c) Returning to the $24\ \text{V}$ battery, we place a second identical resistor after the first one along the same path. Reason what happens to the total resistance and calculate the new current.