Series and parallel circuits
On an old string of Christmas lights in a Galway living room, if one bulb blows, they all go out. But when a bulb blows in the kitchen at home, the other lights stay on. The difference lies in how they are connected: in series or in parallel.
Series circuit: a single path
If you connect one bulb to a battery it shines brightly, but when you place a second bulb on the same wire after it, both glow more dimly. Why does adding components in a line reduce the current in the whole circuit?
The brightness of a bulb depends on the power it transforms, $P = VI = I^2R$: the larger the power, the brighter the bulb. So to compare brightness, compare the power in each bulb.
Why derive it? In series the same current $I$ flows through every resistor (charge is conserved), and the voltages add because of conservation of energy: each charge gives up energy in each resistor in turn, so the energy per unit charge supplied by the battery equals the sum of the p.d.s: $V = IR_1 + IR_2 = I(R_1 + R_2)$, so $R_{eq} = R_1 + R_2$. You can check this with primary data: measure $V$ and $I$ for each resistor and for the pair; the readings of $I$ agree at every point, and $V/I$ for the pair equals $R_1 + R_2$.
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 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 of $2\ \Omega$ and $3\ \Omega$ are connected in series, as shown in the figure.
What is the total (equivalent) resistance of the combination?
In which type of connection does current have only one possible path, series or parallel? And in which can it be split among several branches?
In which type of connection does current have only one possible path, series or parallel? And in which can it be split among several branches?
A simple torch has a battery, a switch and a light bulb. a) Are they connected in series or in parallel? b) What happens to the current when we open the switch?
A simple torch has a battery, a switch and a light bulb.
- a) Are they connected in series or in parallel?
- b) What happens to the current when we open the switch?
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. a) Calculate the equivalent…
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.
- a) Calculate the equivalent resistance.
- b) Calculate the current flowing through the circuit.
- 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.
Parallel circuit: several paths
If you have one bulb lit and you connect another identical one directly to the same terminals of the battery using separate wires, both shine at the original full brightness: why does each bulb still receive the full voltage of the battery, even though the battery now has to supply more current?
Why derive it? Each branch has the same voltage $V$ (same two points), and by conservation of charge the total current is the sum of the branch currents: $I = \dfrac{V}{R_1} + \dfrac{V}{R_2} = V\left(\dfrac{1}{R_1} + \dfrac{1}{R_2}\right)$. Comparing with $I = V/R_{eq}$ gives the formula. In parallel the total current splits at the junction, so $I = I_1 + I_2$. You can verify this with primary data: with an ammeter in each branch and one by the battery, the branch readings add up to the total, and $V/I_{total}$ equals $R_{eq}$.
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…
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. a) What voltage is across the ends of each one? b)…
Two resistors, $R_1 = 6\ \Omega$ and $R_2 = 12\ \Omega$, are connected in parallel to a $12\ \text{V}$ battery.
- a) What voltage is across the ends of each one?
- b) Calculate the current flowing through each branch.
- 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…
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.
We want to measure the total current supplied by a battery in a circuit with two light bulbs in parallel, as shown in the figure. a) Where should we place the ammeter:…
We want to measure the total current supplied by a battery in a circuit with two light bulbs in parallel, as shown in the figure.
- a) Where should we place the ammeter: in one of the branches or next to the battery, before the path divides?
- b) What would the device measure in each of those two positions?
A resistor of $6\ \Omega$ and another of $3\ \Omega$ are connected in parallel. a) Calculate the equivalent resistance. b) Verify that it is even smaller than the…
A resistor of $6\ \Omega$ and another of $3\ \Omega$ are connected in parallel.
- a) Calculate the equivalent resistance.
- b) Verify that it is even smaller than the smaller of the two.
- c) Explain, thinking about the paths available for the current, why adding a branch in parallel always makes it easier for current to flow.
What happens if a bulb blows
The old set of fairy lights is wired in series; the lights in the school classroom are wired in parallel.
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…
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 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. a) Are they connected in series or in parallel? b) Justify your answer by…
In the classroom there are six LED tubes, and when one breaks down, the others remain on.
- a) Are they connected in series or in parallel?
- b) Justify your answer by explaining what happens to the current when one fails.
Two identical light bulbs in series are connected to a $9\ \text{V}$ battery. a) Without knowing their resistance, reason how the voltage is shared between them. b) How…
Two identical light bulbs in series are connected to a $9\ \text{V}$ battery.
- a) Without knowing their resistance, reason how the voltage is shared between them.
- b) How many volts are across each one?
- c) How would the sharing change if the bulbs were different?
Why the wiring at home is in parallel
Irish homes use $230\ \text{V}$ mains, and a Type G plug has a fuse (usually $13\ \text{A}$). For safety, the earth wire connects the metal case of an appliance to earth, so a fault sends current to earth instead of through you. An MCB (miniature circuit breaker) in the consumer unit trips if a circuit carries too much current, and an RCD (residual current device) cuts the power if some current leaks away, for example through a person. Go back to the start: the kitchen lights stay on because each is on its own branch.
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…
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 $6\ \Omega$. a) What current flows through each…
The two headlights of a car are connected in parallel to the $12\ \text{V}$ battery, and each one has a resistance of $6\ \Omega$.
- a) What current flows through each headlight?
- b) What is the total current supplied by the battery with both headlights on?
- c) If one headlight burns out, what happens to the other? Justify your answer considering the type of connection.
You are going to illuminate two scale models with one bulb each, and they must be able to be switched on and off separately using a single battery. a) Would you connect…
You are going to illuminate two scale models with one bulb each, and they must be able to be switched on and off separately using a single battery.
- a) Would you connect them in series or in parallel? Why?
- b) What advantage does your choice have if a bulb blows?
- c) What disadvantage does it pose for the battery life? Relate this to the total current supplied.
In a home, the oven ($23\ \Omega$) and the microwave ($46\ \Omega$) are connected in parallel to the $230\ \text{V}$ mains. a) Calculate the current flowing through each…
In a home, the oven ($23\ \Omega$) and the microwave ($46\ \Omega$) are connected in parallel to the $230\ \text{V}$ mains.
- a) Calculate the current flowing through each appliance when they operate simultaneously.
- b) What total current enters through the kitchen circuit?
- c) Reason why it is convenient for them to be in parallel rather than in series, considering the voltage that each appliance requires.
Combining several resistors
In a series circuit with identical bulbs, the voltage is shared equally; with different resistances, the larger resistance gets the larger share ($V = IR$ with the same $I$).
Three light bulbs of $2\ \Omega$ each are connected in series to a $12\ \text{V}$ battery, as shown in the figure. a) Calculate the total resistance. b) What current…
Three light bulbs of $2\ \Omega$ each are connected in series to a $12\ \text{V}$ battery, as shown in the figure.
- a) Calculate the total resistance.
- b) What current passes through them?
- c) What voltage is across each light bulb?
You have a $6\ \text{V}$ battery and two identical $6\ \Omega$ light bulbs, as shown in the figure. a) If you connect them in series, what current flows through each…
You have a $6\ \text{V}$ battery and two identical $6\ \Omega$ light bulbs, as shown in the figure.
- a) If you connect them in series, what current flows through each one?
- b) If you connect them in parallel, what current flows through each one?
- c) In which setup do they shine brighter? Justify your answer using the results.
We connect identical $3\ \Omega$ light bulbs in series to a $9\ \text{V}$ battery, adding one at a time. a) Calculate the circuit current with one, with two and with…
We connect identical $3\ \Omega$ light bulbs in series to a $9\ \text{V}$ battery, adding one at a time.
- a) Calculate the circuit current with one, with two and with three light bulbs.
- b) What happens to the brightness of the bulbs as we add more in series?
- c) Explain the result using equivalent resistance and Ohm's law.
Now we connect identical $12\ \Omega$ light bulbs in parallel to a $6\ \text{V}$ battery, adding one at a time. a) What current passes through each bulb when there are…
Now we connect identical $12\ \Omega$ light bulbs in parallel to a $6\ \text{V}$ battery, adding one at a time.
- a) What current passes through each bulb when there are one, two or three?
- b) Calculate the total current supplied by the battery in each case.
- c) Reason why the battery runs out faster the more bulbs we connect in parallel.
Three resistors of $2\ \Omega$, $4\ \Omega$ and $4\ \Omega$ are in parallel, as shown in the figure. a) Calculate the equivalent resistance using…
Three resistors of $2\ \Omega$, $4\ \Omega$ and $4\ \Omega$ are in parallel, as shown in the figure.
- a) Calculate the equivalent resistance using $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$.
- b) If the combination is connected to a $6\ \text{V}$ battery, what total current flows?
- c) Calculate the current in each branch and check that the three sum to the total current.