# Calculating Total Resistance in a Circuit: Delta - Y Formula or Simpler Method?

• songoku
In summary, the delta-Y method is easier to solve, but the series-parallel reduction method is easier to perform and less error-prone.
songoku
Homework Statement
(See picture below)

Find current flowing through 14 - ohm resistor
Relevant Equations
V = I.R

Series and parallel combination

Delta - Y configuration?

To find total resistance between 22 Ω, 14 Ω and 4.5 Ω should I use delta - Y formula? Or there is other simpler way?

Thanks

Don't let yourself be fooled: Redraw with the 22 ##\Omega## and 14 ##\Omega## upright.

songoku
BvU said:
Don't let yourself be fooled: Redraw with the 22 ##\Omega## and 14 ##\Omega## upright.
... which can be done by a combination of shrinking a zero resistance wire down to a node and expanding a node into a zero resistance wire, both of which are always legal.

songoku
BvU said:
Don't let yourself be fooled: Redraw with the 22 ##\Omega## and 14 ##\Omega## upright.
haruspex said:
... which can be done by a combination of shrinking a zero resistance wire down to a node and expanding a node into a zero resistance wire, both of which are always legal.
My god, it will only be parallel then series then parallel again.

Let say I want to continue my foolish idea. Can it be done using delta - Y formula?

Thanks

Delta2
You can always try -- and checking the answer is easy now that you have it

songoku
BvU said:
You can always try -- and checking the answer is easy now that you have it
I got different answers. Why can't I use delta - Y formula?

Thanks

The problem with a wye-delta transform is that you are transforming the resistor in question, the 14 ohm resistor will no longer be 14 ohms and it's current will be different. You will get a solution to the equivalent network, and the currents in the branches outside of the delta will be correct. But you will then have to transform back to delta to find the current in the 14 ohm resistor.

Plus, it's not clear to me the one version is any easier to solve than the other.

songoku
songoku said:
Why can't I use delta - Y formula?
You can. We can't see what went wrong unless you post your work.

Also, your original series-parallel reduction method is much easier and less error-prone than the delta-Y method.
Nevertheless, it is good to try different methods and verify your answer.
Please post both your solutions so we can point out the error.

songoku, Delta2 and BvU
I understand.

Thank you very much for the help BvU, haruspex, daveE, cnh 1995

BvU

## 1. What is the definition of net resistance in a circuit?

The net resistance of a circuit is the total resistance that a current encounters as it flows through the circuit. It is measured in ohms (Ω) and is calculated by adding up the individual resistances of all the components in the circuit.

## 2. How is net resistance different from individual resistances?

Individual resistances refer to the resistance of each component in a circuit, while net resistance is the combined resistance of all the components. Net resistance takes into account the effects of both series and parallel connections between components.

## 3. What factors affect the net resistance of a circuit?

The net resistance of a circuit is affected by the type of material the components are made of, the length and thickness of the wires connecting the components, and the arrangement of the components (series or parallel).

## 4. How do you calculate the net resistance of a circuit?

To calculate the net resistance of a circuit, you can use Ohm's Law (R = V/I) for series connections and the reciprocal formula (1/R = 1/R1 + 1/R2 + ...) for parallel connections. Once you have calculated the individual resistances, you can add them together to get the net resistance.

## 5. Why is it important to know the net resistance of a circuit?

Knowing the net resistance of a circuit is important because it helps determine the amount of current that will flow through the circuit. It also allows us to calculate the power dissipated by the circuit and to choose the appropriate components for a specific application.

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