# Current division, equivalent resistances and short circuts

• JasonHathaway
In summary: How does the current flows or divides in the circuit? does the current flow normally through any line even if there isn't any resistor in it?2- Is this case the same for the following?- A wire is the same as a zero ohm resistance. more importantly, any path created by continuous wiring comprises a single node. connections of components to a node may be made anywhere, and you are free to move the connection points to anyplace along the continuous path. that means that you can reorganize the circuit
JasonHathaway
Hi everyone, this my first post in here.

Anyway, this is a solved problem, but I can't get the answer :S

## Homework Equations

* Series-Parallel combination (RT=R1+R2+R3...+Rn for series, 1/RT=1/R1+1/R2+1/R3...+1/Rn for parallel)

* WYE (TEE) - DELTA (PI) Transformations:

1- WYE (TEE) to DELTA (PI): Each resistor in the DELTA (PI) is equal to the sum of all possible products of WYE (TEE) resistors taken two at a time, divided by the opposite WYE (TEE) resistor.

2- DELTA (PI) to WYE (TEE): Each resistor in the WYE (TEE) is equal to the product of the resistors in two adjacent DELTA (PI) branches, divided by the sum of all three DELTA (PI) resistors.

## The Attempt at a Solution

I've tried to solve using two methods above, and I've ended up with 27.14 ohm for the equivalent resistance with both methods. When I looked at the solution above, I saw that the line the two 20 ohms resistors was not ignored (I though that as long as there is not resistor in a line, it can be ignored), but instead it was assumed that there was a 0 ohm resistor.

so my questions are:

1- How does the current flows or divides in the circuit? does the current flow normally through any line even if there isn't any resistor in it?

2- Is this case the same for the following?

A wire is the same as a zero ohm resistance. More importantly, any path created by continuous wiring comprises a single node. Connections of components to a node may be made anywhere, and you are free to move the connection points to anyplace along the continuous path. That means that you can reorganize the circuit diagram in any way you wish (to make more obvious series or parallel relationships) so long as the individual components retain their connections to the same nodes. Feel free to bend or stretch the wires to any shape you want, too.

Both of the circuits you show can be solved without resorting to Y or Δ transformations simply by reorganizing some of the components according to the above rules. Start by labeling the individual nodes so that you can recognize them and confirm that any component movements retain the same node affiliations.

See if you can "move" the 5Ω resistor and the right-hand 20Ω resistor to new locations that will make obvious some series or parallel opportunities.

#### Attachments

• Fig1.gif
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I got the idea, thanks :)

## What is current division?

Current division is the distribution of current in a parallel circuit where the total current is divided among multiple branches based on their resistances.

## How do I calculate equivalent resistance in a parallel circuit?

To calculate the equivalent resistance in a parallel circuit, you can use the formula 1/Req = 1/R1 + 1/R2 + ... + 1/Rn, where Req is the equivalent resistance and R1, R2, etc. are the individual resistances in the circuit.

## What is the purpose of short circuits in a circuit?

Short circuits occur when there is a low resistance path in a circuit, causing a large current to flow. They can be used to protect devices from damage by quickly redirecting the current away from them.

## How do I calculate the total current in a parallel circuit?

The total current in a parallel circuit is equal to the sum of the currents in each branch. This can be calculated using the formula Itotal = I1 + I2 + ... + In, where Itotal is the total current and I1, I2, etc. are the individual currents in each branch.

## How can I determine the voltage drop across a short circuit?

The voltage drop across a short circuit can be calculated using Ohm's Law (V = IR), where V is the voltage drop, I is the current flowing through the short circuit, and R is the resistance of the short circuit. The voltage drop will be equal to the product of the current and the resistance.

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