Series and parallel circuits

Two light bulbs are connected in series, one after the other, to a battery, as shown in the figure.

Through which of the two does more current flow? Justify your answer.

Two resistors of $2\ \Omega$ and $3\ \Omega$ are connected in series, as shown in the figure.

What is the total (equivalent) resistance of the combination?

Two resistors, $R_1 = 2\ \Omega$ and $R_2 = 4\ \Omega$, are connected in series to a $12\ \text{V}$ battery, as shown in the figure.

1. a) Calculate the equivalent resistance.
2. b) Calculate the current flowing through the circuit.
3. c) Find the voltage across each resistor using Ohm's law and verify that the two voltages add up to the $12\ \text{V}$ of the battery.

Two light bulbs are connected in parallel to the same battery, each along its own path, as shown in the figure.

What do they have in common electrically: the current passing through them or the voltage across their ends? Explain.

Two resistors, $R_1 = 6\ \Omega$ and $R_2 = 12\ \Omega$, are connected in parallel to a $12\ \text{V}$ battery.

1. a) What voltage is across the ends of each one?
2. b) Calculate the current flowing through each branch.
3. c) What is the total current supplied by the battery?

Two resistors of $4\ \Omega$ and $12\ \Omega$ are in parallel. Knowing that in this setup $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$ holds, calculate the equivalent resistance of the combination.

In an old set of fairy lights, the bulbs are connected in series, as shown in the figure.

If one bulb blows and its filament breaks, what happens to the others? Explain thinking about the path followed by the current.

In a scale model, two light bulbs are connected in parallel to a battery. If you unscrew one of them, what happens to the other? Justify your answer.

In the classroom there are six LED tubes, and when one breaks down, the others remain on.

1. a) Are they connected in series or in parallel?
2. b) Justify your answer by explaining what happens to the current when one fails.

In homes, sockets and lamps are connected in parallel and not in series. Give a reason thinking about what would happen when switching off an appliance or if one breaks down.

The two headlights of a car are connected in parallel to the $12\ \text{V}$ battery, and each one has a resistance of $6\ \Omega$.

1. a) What current flows through each headlight?
2. b) What is the total current supplied by the battery with both headlights on?
3. c) If one headlight burns out, what happens to the other? Justify your answer considering the type of connection.

In a home, the oven ($23\ \Omega$) and the microwave ($46\ \Omega$) are connected in parallel to the $230\ \text{V}$ mains.

1. a) Calculate the current flowing through each appliance when they operate simultaneously.
2. b) What total current enters through the kitchen circuit?
3. c) Reason why it is convenient for them to be in parallel rather than in series, considering the voltage that each appliance requires.

We connect identical $3\ \Omega$ light bulbs in series to a $9\ \text{V}$ battery, adding one at a time.

1. a) Calculate the circuit current with one, with two and with three light bulbs.
2. b) What happens to the brightness of the bulbs as we add more in series?
3. c) Explain the result using equivalent resistance and Ohm's law.

Three resistors of $2\ \Omega$, $4\ \Omega$ and $4\ \Omega$ are in parallel, as shown in the figure.

1. a) Calculate the equivalent resistance using $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$.
2. b) If the combination is connected to a $6\ \text{V}$ battery, what total current flows?
3. c) Calculate the current in each branch and check that the three sum to the total current.

A classmate states: "In series, the current from the battery is shared between the bulbs."

1. a) Is he right?
2. b) With a $12\ \text{V}$ battery and two $3\ \Omega$ light bulbs in series, calculate the current passing through each one and the voltage across each one.
3. c) Correct your classmate's statement: what is actually shared in a series circuit?