Smaller. Each branch you add is an extra path for the charge, so at the same voltage more current flows, and that means a smaller resistance. Two resistors of 100 ohms in parallel are 50 ohms together. Calculate with one divided by R total equals one divided by R one plus one divided by R two.
This video can also be listened to in العربية, English, Français and Türkçe. Choose your language under the gear icon in the player, at Audio track and Subtitles.
You have a resistor of 100 ohms and put a second one of 100 ohms beside it, so the current can go through both. How big is the resistance together? Not 200 ohms, and not 100 either: together they are 50 ohms.
If each component is in its own branch, side by side between the same two points, that is called a parallel circuit. Where the branches begin the current splits, and further on it comes back together. That split is called current division, and the current through one branch is a branch current. The branch currents add up to the total current: I total equals I one plus I two.
What is not divided is the voltage. Each branch has both its ends on the same two points, so every branch has the same voltage across it: U total equals U one equals U two.
Each branch you add is an extra path for the charge. At the same voltage more current then flows, and more current at the same voltage means a smaller resistance. In general you work with one divided by R total equals one divided by R one plus one divided by R two, and at the end you turn that result upside down. So the total resistance is always smaller than the smallest resistance in the circuit.
In the worked example, 30 ohms and 60 ohms are in parallel on 12 volts. Both have 12 volts across them, so 0.40 amperes flows through the 30 ohms and 0.20 amperes through the 60 ohms: the largest current goes through the smallest resistance. Together 0.60 amperes, and the total resistance is 20 ohms, smaller than the 30.
For upper secondary physics, in electricity.
In this video
The full explanation, in writing
Adding a hundred ohms
0:00A resistor of a hundred ohms. You put a second one of a hundred ohms beside it, so the current can go through both. What is the total resistance? Have a guess.
Several paths
0:15If each component is in its own branch, side by side between the same two points, that is called a parallel circuit. The current splits where the branches begin, and comes back together further on. That split is called current division, and the current through one branch is a branch current.
0:32Together the branch currents equal the total current: I total equals I one plus I two. What is not divided is the voltage. Each branch has both its ends on the same two points, so every branch has the same voltage across it: U total equals U one equals U two.
An extra path
0:53Each branch you add is an extra path for the charge. At the same voltage, more current then flows, and more current at the same voltage means a smaller resistance. Two resistors of a hundred ohms side by side are fifty ohms together: half. In general you work with one divided by R total equals one divided by R one plus one divided by R two.
1:17So the total resistance is always smaller than the smallest resistance in the circuit. Your turn. A resistor of thirty ohms and one of sixty ohms are in parallel across twelve volts. Which of the two carries the largest current?
Thirty and sixty ohms
1:36With the one-divided-by formula, you first work out one divided by R total, and then you turn it upside down. Both have twelve volts across them. The thirty-ohm resistor gets twelve divided by thirty: zero point four zero amperes. The sixty-ohm resistor: twelve divided by sixty, zero point two zero amperes.
1:57The largest current goes through the smallest resistance. Together that is zero point six zero amperes. And the total resistance: one divided by thirty plus one divided by sixty is three sixtieths, and that is one divided by twenty. R total is twenty ohms, smaller than the thirty ohms.
2:16Twelve volts divided by twenty ohms again gives zero point six zero amperes, exactly the total current.
Three things to remember
2:23Three things. In a parallel circuit every branch has the same voltage across it. The current divides: the branch currents add up to the total current, and the largest current goes through the smallest resistance. And you calculate the total resistance with one divided by R total equals one divided by R one plus one divided by R two.
2:45It is always smaller than the smallest resistance.
Two questions
2:49Two questions. One. A resistor of twenty ohms and one of eighty ohms are in parallel across eight point zero volts. What is the total resistance? Two. You add a third resistor in parallel. What happens to the total current, and to the current through the other two?
The answers
3:10The first: one divided by twenty plus one divided by eighty is five eightieths, and that is one divided by sixteen. R total is sixteen ohms. It checks out via the currents too: zero point four zero plus zero point one zero is zero point five zero amperes, and eight point zero divided by zero point five zero is sixteen ohms.
3:32The second: the total current gets larger, because a branch current is added. The current through the other two stays the same, because the voltage across their branch does not change.
When series and parallel are mixed
3:43How to calculate a circuit in which series and parallel are mixed: there is a separate video on the channel about series-parallel circuits.
Frequently asked questions
How do you calculate the total resistance of a parallel circuit?
With one divided by R total equals one divided by R one plus one divided by R two. Watch the last step: at that point you have worked out one divided by R total, so you still have to turn that fraction upside down. For 30 ohms and 60 ohms that is one thirtieth plus one sixtieth, together three sixtieths, which is one twentieth, so R total is 20 ohms.
Why does the resistance get smaller when you add a resistor in parallel?
Because each branch is an extra path for the charge. At the same voltage, more current flows through two paths together than through one, and more current at the same voltage means, by definition, a smaller resistance. That is why the total resistance is always smaller than the smallest resistance in the circuit.
What is a branch current?
The current through one branch of a parallel circuit. Where the branches begin the current splits, and that is called current division. Together the branch currents add up to the total current: I total equals I one plus I two.
Is the voltage the same across every branch of a parallel circuit?
Yes. Each branch has both its ends on the same two points, so every branch has the same voltage across it: U total equals U one equals U two. That is exactly the opposite of a series circuit, where the voltage is shared and the current is the same everywhere.
Which resistor gets the largest current?
The smallest one. Both branches have the same voltage across them, and with I equals U divided by R the smallest R gives the largest I. For 30 ohms and 60 ohms on 12 volts that is 0.40 amperes through the 30 ohms and 0.20 amperes through the 60 ohms.
Before this came the series circuit: all components one after another in one circuit, where the resistances add up instead. Next: a circuit in which series and parallel are mixed, and how to reduce it step by step to a single resistance.
This video carries audio and subtitles in several languages. Pick yours under the gear icon in the player, at Audio track and at Subtitles.
Physics with Thomas: physics explained with pictures where they add something, and without them where they distract.
In this series
Electric current6:12
Voltage and capacity4:43
Connecting ammeter and voltmeter4:10
Resistance and Ohm's law4:21
Resistance of a wire4:40
Variable resistor, NTC, PTC and LDR3:40
Series circuit3:32
Parallel circuit3:56
Series-parallel circuit3:37
Circuits practical test5:13
Power2:58
Kilowatt-hour3:05
About me
My name is Thomas Schuurmans, and I have a passion for physics and for understanding why things work the way they do. What I want is to get young people asking “why is that?” and “how does that work?” more often, and to hand them the tools of physics in a way that is simple and that you can see.
I graduated in applied physics at Delft University of Technology in 2003. After that I spent more than twenty years outside education: first at TNO, the Dutch applied research institute, then at a design agency, and eventually founding Proportion Global, through which I work on innovation questions in Africa, Latin America and South Asia. That work resembles physics more than you would expect: don't start from a solution, first understand what is going on, try something, be wrong, and look again.
Since 2026 I have been teaching physics to both lower and upper secondary classes, and I started a master's at the University of Amsterdam for my full teaching qualification. That is where I learned that a secondary school pupil's real attention for new material lasts about seven minutes. And my own weakness happens to be telling too many side stories.
That is where the idea came from: videos that explain one topic sharply and visually, inside those seven minutes. I make them for my own pupils. Then I publish them, because good explanation should be within reach of anyone who needs it, wherever you live and whatever language you think and speak in.