Paralell and series cicuits HELP

[raa849]

Homework Statement

"two identical loads in parallel have a greater total current than when they are connected in series"

we have to prove this statement right or wrong.

Homework Equations

The Attempt at a Solution

 

[LowlyPion]

Welcome to PF.

So what are your thoughts on it?

 

[raa849]

please? anyone?

 

[berkeman]

please? anyone?

You are required to do the work. We do not do your homework/coursework for you. Pleae re-read the Rules link at the top of the page, and then come back here and post your thoughts and an attempt at a solution. Then we can offer some hints and tutorial thoughts.

 

[raa849]

1. Homework Statement

"two identical loads in parallel have a greater total current than when they are connected in series"

and we have to prove this statement right or wrong


2. Homework Equations



3. The Attempt at a Solution

this statement is right ...the parallel has a greater current because both resistors are connected to the source instead of the series because there is only one connection with the series

 

[berkeman]

1. Homework Statement

"two identical loads in parallel have a greater total current than when they are connected in series"

and we have to prove this statement right or wrong


2. Homework Equations



3. The Attempt at a Solution

this statement is right ...the parallel has a greater current because both resistors are connected to the source instead of the series because there is only one connection with the series

Thank you, that's better. I think you'll need to give a more rigerous proof to get full credit on your problem, though. First of all, is it only supposed to apply to resistors as the "Loads"? That makes it easier if it does. If not, you can still use the term Z for a generalized impedance load.

I think it would help your proof if you wrote out the series and parallel combination equations for resistors. Call the resistors R (they are equal in this problem). Then compare the two equations mathematically, showing that one is always bigger than the other, except for the degenerate case when they are both zero.

 

[raa849]

http://hades.mech.northwestern.edu/wiki/images/5/51/Series_parallel_resistors.gif


ok! yes an equation will really be able to prove the statement right.
i hope my picture above turns out right. is this the type of equation your talking about.

but instead use:

series
resistance total= R1+R2

parallel
resistance total = (1/R1+1/R2)-1


what number could i use so that parallel resistance is more. would i just use any numbers?

 

[LowlyPion]

Since the individual loads are the same, you might compare what the equivalent load is in the equations you cite, showing numerically that one is greater than the other.

 

[epenguin]

No, that is actually not the formula for parallel resistance!

 

[raa849]

how does this sound?

There are two very simple circuits, a simple circuit and a parallel circuit. In a parallel circuit, each load is directly connected to the power source. The voltage is equal across all components in the circuit. In a series circuit, the current must flow through one load to get to the next load. So the amount of current is the same through all the resisters.
The statement, “Two identical loads in a parallel have a greater total current than when they were connected in series” can be proven correct by using the Junction Rule. The junction rule says that resisters in series have the same current and resisters in parallel have the same voltage drop. So it is true that the total current will be greater for the entire circuit if the loads are connected in parallel because the resistance of the current drops when a parallel arrangement is used. By using Ohms law we can find the resistance for both series and parallel circuits. For series circuits, resistance = R1+R2+R3...etc. But for parallel circuits, total resistance = 1/R1+1/R2+1/R3...etc.

 

[mikelepore]

But for parallel circuits, total resistance = 1/R1+1/R2+1/R3...etc.

That sentence is not correct.

 

[LowlyPion]

The picture provided shows the correct formula.

Perhaps the exponent^-1 is being forgotten?

 

[epenguin]

You have no way of knowing one way or the other?