• Skip to main content
  • Skip to secondary menu
  • Skip to primary sidebar
  • Skip to footer

Power Inception

Resources for All Things Power Related

  • Home
  • Tech News
  • Product Reviews
  • Refrigerators
  • DC Circuits
  • Networking
  • Physics
  • Apps
  • Business

Delta to wye and wye to delta conversion

04/09/2013 By PowerInception.com

Sometimes we are not sure in electric circuits that the resistors are neither in parallel nor in series.

See the circuit below here the relation between R1 resistor and R6 resistor is series or parallel we are not sure.

delta to wye

In that case we can simplify this circuit using three terminal equivalent networks. Three terminal networks are used in three phase connection, matching networks and electrical filters.

Figure 2 shows Wye (Y) and Tee (T) networks and figure 3 shows delta (∆) and pie (Π) network.

delta wye conversion

delta wye transformation

These networks are the equivalent of large network. I will discuss here how to transform wye to delta and delta to wye.

Delta to wye conversion

It is easy to work with wye network. If we get delta network, we convert it to wye to work easily. To obtain the equivalent resistance in the wye network from delta network we compare the two networks and we confirm that they are same. Now we will convert figure 3 (a) delta network to figure 2 (a) wye network.

From figure 3 (a) for terminals 1 and 2 we get,

R12 (∆) = Rb || (Ra + Rb)

From figure 2 (a) for terminals 1 and 2 we get,

R12(Y) = R1 + R3

Setting wye and delta equal,

R12(Y) = R12 (∆) we get,

1

2

Equations (v), (vi) and (vii) are the equivalent resistances for transforming delta to wye conversion. We do not need to memorize these equations. Now we create an extra node shown in figure 4 and follow the conversion rule,

Each resistor in the Y network is the product of the resistors in the two adjacent Del branches, divided by the sum of the three Del resistors.

delta wye conversion

Now we will solve a problem how to convert delta to wye network. It will give clear concept.

Problem: convert the delta network to wye network.

del to wye conversion problem

From equation (v), (vi) and (vii) we can find the equivalent resistance of wye network,

3

The equivalent Y network configuration is shown in figure 6.

delta to wye conversion problem solution

Wye to delta conversion

For conversion to wye network to delta network adding equations (v), (vi) and (vii) we get,

 R1R2 + R2R3 + R3R1 = RaRbRc(Ra +Rb + Rc)/(Ra + Rb + Rc)2

                                = RaRbRc/(Ra + Rb + Rc) —————— (ix)

Dividing equation (ix) by each of the equations (v), (vi) and (vii) we get,

Ra = R1R2 + R2R3 + R3R1/ R1

Rb = R1R2 + R2R3 + R3R1/ R2

Rc = R1R2 + R2R3 + R3R1/ R3

For Y to delta conversion the rule is followed below,

Each resistor in the delta network is the sum of all possible products of Y resistors taken two at a time, divided by the opposite Y resistor.

Delta and Y are said to be equal or balanced when

R1 = R2 = R3 = RY, Ra = Rb = Rc = R∆

For these condition conversion formulas become,

           RY = R∆/3

Or     R∆ = 3RY

Here Y connection is like series connection. And Del is like parallel connection.

Filed Under: DC Circuits Tagged With: delta to wye

Primary Sidebar

How to Become a Scientist

Are you wondering how to become a scientist? If you have a scientific mind and are interested in chemistry, physics, earth sciences, astronomy, or more, working as a scientist might be a great fit. You can work in a range of industries, performing all kinds of fascinating tasks, and be paid well for your effort. […]

The Complete Guide to Purchasing Two-Way Radios for Businesses

5 Key Benefits of a GPS Asset Tracker

Document Security Mistakes

4 Common Document Security Mistakes to Avoid for Your Business

Well Drilling Contractor

5 Tips for Hiring a Well Drilling Contractor

Emerging Trends in Business

How to Keep up With Emerging Trends in Business

3D Printing Services

How to Pick 3D Printing Services: The Complete Guide for Businesses

Product Reviews for Small Businesses

6 Tips on Managing Product Reviews for Small Businesses

Buy Chemicals Online

Can You Buy Chemicals Online? Legality and Considerations

Best ups for gaming computer

10 Best UPS For Gaming PC For Ultimate Backup Power

best Power Probe 3 Master Kit

Best Power Probe Master Kit Reviews And Buying Guide

Best Circuit Breaker Panels

Proven 10 Best Circuit Breaker Panel For Ultimate Protection

Footer

About us

PowerInception.com provides thorough tech reviews and the latest technology news. I participate in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to amazon.com. As an Amazon Associate I earn from qualifying purchases.

Privacy policy

Affiliate Disclosure

Contact us

Popular posts

3D Printing Services

How to Pick 3D Printing Services: The Complete Guide for Businesses

Product Reviews for Small Businesses

6 Tips on Managing Product Reviews for Small Businesses

Buy Chemicals Online

Can You Buy Chemicals Online? Legality and Considerations

Best ups for gaming computer

10 Best UPS For Gaming PC For Ultimate Backup Power

best Power Probe 3 Master Kit

Best Power Probe Master Kit Reviews And Buying Guide

Categories

  • AC Circuits (1)
  • Apps (16)
  • Battery (4)
  • Business (77)
  • DC Circuits (19)
  • Digital electronics (13)
  • Economics (2)
  • Electrical & Electronics (20)
  • Featured (15)
  • Financial Tech (6)
  • Generator (7)
  • Networking (16)
  • Payroll and HR (4)
  • Physics (30)
  • Product Review (30)
  • Programming C (2)
  • Refrigerators (4)
  • Renewable Energy Technology (3)
  • Software (25)
  • Tech News and Reviews (84)
  • Transformers (6)
  • Websites and Internet (19)

Copyright © 2023 Power Inception