Competition - post a photo you've taken of nature >>

Past Paper question about Resistance, please explain why the current is divided by 4.

I have attached both question and mark scheme to this message so you can see them.
The correct solution is 230(V)/6.5(A), which equals 35ohms to two significant figures.

I understand that you cannot divide by the full 26amps, because you only want the resistance of ONE heating element, not all 4, so you divide by 6.5 because 26/4=6.5. However, I don't get why you only divide the current by 4 and not the voltage too?

For one resistor, why do you divide the current by 4 but not the voltage by 4 too? Can somebody please explain? Thanks!

Screenshot_144.png67.3KB

Screenshot_1.png22.3KB

Reply 1

solC

Original post by blobbybill

Since it is a parallel circuit, the voltage across each branch has to be the same.
Imagine each coulomb moving around the circuit carrying 230 Joules of energy, when it reaches the part where the circuit splits, it can only pick one branch to go through. Therefore it carries all the energy it has through that one branch, so in this case the whole 230J. Thus the voltage across the one resistor it passes is 230V (by definition of the volt).
Do you understand now? :smile:

Reply 2

blobbybill

Original post by solC

Sort of. I get that the whole 230V would pass through 1 resistor, but why doesn't the current all pass through 1 resistor like the voltage does? Why is the current split evenly between the resistors at all times?
Thanks

Reply 3

BobBobson

The way I did it, was that since theres 26 A in total going round the circuit, there is 26 / 4 A coming out of each resistor. So therefore the resistance of each resistor would be 230 / (26/4).

Reply 4

Smithenator5000

Original post by blobbybill

Hello there,

To understand this, it may help to consider the respective definitions of current and potential difference. The electrical current is a measure of how much charge passes a point per unit time. At the point just before the circuit branches off, there are

26 C

of charge flowing every second. When the circuit does branch off, as no charges have been created or destroyed, only one quarter of that charge can flow down each respective path. It splits evenly because the resistance of each path is the same and there is thus no preference for any particular electron. Because potential difference is a measure of energy per unit charge, even though the current through each resistor is smaller than the original current, the amount of energy has been scaled accordingly with the reduced charge. If this needs further elaboration, please ask.

I hope that this has been helpful,

Smithenator5000

(edited 7 years ago)

Reply 5

LMcK20

It's one of Kirchoff's laws in a parallel circuit I(total) =I (1) + I (2) so the current is divided throughout the circuit

Reply 6

solC

Original post by blobbybill

In a parallel circuit, each coulomb chooses the path of least resistance.
Let's say each coulomb is a car, and it reaches a junction where it can choose to go down two different paths with different amounts of traffic. Of course they're all gonna choose the path with less traffic right?
Now, if the amount of traffic of each path represents the resistance of each branch, then we can see that the current along each branch is gonna be inversely proportional to its resistance, i.e. the higher the resistance the lower the current.
So since each branch has the same resistance in this case, the flow of electrons (current) will be the same through each one.

Hopefully that makes some sense :tongue:

Reply 7

Joinedup

Original post by blobbybill

IMO you should get out of the habit of saying 'voltage through' before this will start to make sense

Current is simply a flow - it's absolutely correct to talk about the current flowing through a conductor or the current flowing through a resistor.

Voltage (Potential Difference) is a difference in potential between two points - you could think of it as the force that's making the current flow by pushing the charge into the resistor... but it's not the flow itself - voltage doesn't pass (or flow) through a resistor... it exists across the resistor, the difference in potential between one side of the resistor and the other.

Reply 8

blobbybill

Original post by LMcK20

It's one of Kirchoff's laws in a parallel circuit I(total) =I (1) + I (2) so the current is divided throughout the circuit

What about in a series circuit?

Reply 9

BobBobson

Original post by blobbybill

What about in a series circuit?

In a Series circuit, the current is always the same everywhere

Posted from TSR Mobile

Reply 10

username2548927

Original post by blobbybill

If you remember you're rules for current and voltage in series and parallel circuits then this question should be no problem.

Okay here are the rules:

Series circuit:

The current is the same at all points. This means that the current across each electrical component in a circuit is the same for every single component in the circuit. If a circuit has a supply current of 3A then each component in the circuit will have a current of 3A running through it.

For voltage in a series circuit the sum of the voltage across each component adds up to the supply voltage. It's also useful to note that the bigger the share of the resistance a component has the more voltage it has. If a circuit has a supply voltage of 10V an 2 lamps are connected, the sum of these 2 lamps will add up to 10V.

Parallel Circuit:

For current in a parallel circuit the sum of the currents across each branch adds up to the supply current. If a circuit has a supply current of 5A and has two branches connected, then the current in these two branches must add up to 5A.

For voltage in a parallel circuit the voltage across each branch equals the supply voltage. If a circuit has a supply voltage of 10V and 3 branches are connected, it doesn't matter how many branches are connected the voltage across all 3 branches will equal 10V.

In this question you can clearly see there are four branches connected in the circuit. We know that there is a supply voltage and from what I've explained briefly about voltage in a parallel circuit you'll then know that one branches has a voltage of 230V. There is one heating element per branch therefore we know that the the voltage in one heating element must be 230V. To get the current we have to think about the rule for current in a parallel circuit. Since the heating elements are all identical you can get the current by just doing 26/4 = 6.5A because if they're all the same then they must contain equal current and since we know that rule for current in a parallel circuit this is why it is 6.5A. To finalise we now know the current and voltage across one heating element so simply R = V/I = 230/6.5 = 35.4 Ohms

Posted from TSR Mobile

Reply 11

mik1a

Think about the electrons. If five electrons arrive at a fork in the circuit, and two go left, then the other three must go right. Then when those paths rejoin, all five electrons continue on together.

I_total = I(1) + I(2)
5 = 2 + 3

That's Kirchoff's law - electrons always have to go somewhere.