Exercises: 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 current of $0.3\ \text{A}$ flows through a resistor of $20\ \Omega$. Calculate the voltage across its ends.

The bulb of a flashlight has a resistance of $9\ \Omega$ and is connected to a $4.5\ \text{V}$ battery. What current flows through it?

A current of $0.5\ \text{A}$ flows through a resistor connected to a $1.5\ \text{V}$ battery. What is the resistance?

A computer fan operates at $12\ \text{V}$ and has a resistance of $60\ \Omega$. What current does it draw?

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.

We want a current of $1.2\ \text{A}$ to flow through a light bulb of $10\ \Omega$.

1. a) What voltage needs to be applied to it?
2. b) If we only have a $6\ \text{V}$ battery, what resistance should the bulb have for the same current to flow?

A USB charger provides $5\ \text{V}$ and powers an accessory of $250\ \Omega$. Calculate the current it supplies and express it in amperes and in milliamperes.

A resistor of $9\ \Omega$ requires $0.5\ \text{A}$ passing through it to operate correctly.

1. a) What voltage needs to be applied to it?
2. b) Will a $4.5\ \text{V}$ lantern battery be suitable? Justify your answer with calculations.

Two light bulbs, one of $45\ \Omega$ and another of $90\ \Omega$, are connected separately to the same $9\ \text{V}$ battery.

1. a) Calculate the current passing through each one.
2. b) Which one shines brighter? Explain your answer by relating resistance and current.

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.

Emma says: "If we double the voltage, the current also doubles." Liam 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.

Using a $9\ \text{V}$ battery, we measure the current for several resistors: with $3\ \Omega$, $3\ \text{A}$ flows; with $9\ \Omega$, $1\ \text{A}$; and with $18\ \Omega$, $0.5\ \text{A}$.

1. a) Verify that the three measurements satisfy Ohm's law.
2. b) Predict the current for a resistance of $45\ \Omega$.
3. c) What resistance would need to be connected for $0.1\ \text{A}$ to flow?

Use the hydraulic analogy (height of the tank = voltage, flow rate = current, narrowness of the pipe = resistance):

1. a) Explain why increasing the resistance of a circuit decreases the current if the voltage does not change.
2. b) Check this with numbers: calculate the current for a $12\ \text{V}$ battery with resistances of $6\ \Omega$ and $12\ \Omega$.
3. c) After "narrowing the pipe," what could you do to the "tank" to recover the initial flow rate? What does this correspond to in the circuit?

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.