Electric Current and Voltage Division Rule

Current Division Rule When current flows through more than one parallel paths, each of the paths shares a definite porion of th...

Current Division Rule



When current flows through more than one parallel paths, each of the paths shares a definite porion of the total current depending upon the impedance of that path. The definite portion of total current shared by any of the parallel paths can easily be calculated if the impedance of that path and the equivalent impedance of the parallel system are known to us. The rule or formula derived from these known impedances to know the portion of total current through any parallel path is known as current division rule. This rule is very important and widely used in the field of electric engineering in different applications. Actually this rule finds application when we have to find the current passing through each impedance when these are connected in parallel. Let us say, two impedances Z1 and Z2 are connected in parallel as shown below.

A current I passes and is being divided into I1 and I2 at the junction of these two impedances as shown. I1 and I2 pass through Z1 and Z2 respectively. Our aim is to determine I1 and I2 in terms of I, Z1 and Z2.
As Z1 and Z2 are connected in parallel, voltage drop across each will be same. Hence, we can write

Also applying Kirchoff’s current law at junction, we get

We have two equations and can determine I1 and I2.
From (1), we have

Putting this in (2), we get

or,

or,

or,

We have

Putting value of I1, we get


Thus, we have determined I1 and I2 in terms of I, Z1 and Z2.
This rule is applied as follows.
Suppose we have to determine I1. We proceed as

Applying above rule, we will get
Let us apply this rule to some problems.
Let Z1 = 1 + j3, Z2= 3 + j5 and I = 10 Amps.
Applying current divison rule, we will have

Where I1 = current passing through Z1.
Putting given numerical values, we get

Similarly,

The other way to find I2 is as I2 = I – I1 = 10-6.5 + j0.5 = 3.5 + j0.5.
This is how we can apply current division rule.


Voltage Division Rule



Voltage division rule is applied when we have to find voltage across some impedance. Let us assume that the impedances Z1, Z2, Z3,…..Zn are connected in series and voltage source V is connected across them as shown below.

Our aim is to find voltage across some impedance, say, Z3. We see that Z1, Z2, Z3 ….Zn are connected in series. Hence, effective impedance Zeff as seen by the voltage is given by

Current passing the circuit is given by

This current is passing through all the impedances connected in series. Hence, voltage across Z3 is given by

Similarly, voltage across Z1 will be given by

In general, we can write

Where, k = 1, 2, 3,….n and impedances Z1, Z2, Z3 ,…….Zn should be connected in series.
This is called voltage division rule and frequently used to determine the voltage across some impedance. We can write this rule in words as given below.
Voltage across some impedance

COMMENTS

Name

BASIC ELECTRICAL,12,BATTERIES,4,CIRCUIT THEORIES,9,CONTROL SYSTEMS,3,DC MOTOR,1,DIGITAL ELECTRONICS,1,DISTRIBUTED GENERATION,2,DISTRIBUTION,6,ELECTRICAL DRIVES,1,ELECTRICAL LAWS,8,ELECTRONICS DEVICES,2,General,7,GENERATION,3,GENERATOR,1,HIGH VOLTAGE,4,ILLUMINATION,1,INDUCTION MOTOR,7,MATERIALS,1,MEASUREMENT,1,MOTOR,1,POWER ELECTRONICS,2,PROJECTS ON INDUCTION MOTOR,1,PROTECTION,1,SMART GRID,3,SWITCHGEAR,4,SYNCHRONOUS MOTOR,1,TRANSFORMER,6,TRANSMISSION,4,
ltr
item
Electrical for Us: Electric Current and Voltage Division Rule
Electric Current and Voltage Division Rule
https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVAGiJys3wrmz9MQe2T-1Wb7HN88-JHM9XaGKR9x56GFPAWRzQ_K5SM7P4xmlQ6RlFZJy4hovja3h1JK0RWAm-Gz8ttAd0_98J-ClIeBdix9t_odgS6jXgj_AI_qk-LS5nSmDXHiSzuqG9/s320/aid72048-728px-Make-a-Voltage-Divider-Circuit-Step-6.jpg
https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVAGiJys3wrmz9MQe2T-1Wb7HN88-JHM9XaGKR9x56GFPAWRzQ_K5SM7P4xmlQ6RlFZJy4hovja3h1JK0RWAm-Gz8ttAd0_98J-ClIeBdix9t_odgS6jXgj_AI_qk-LS5nSmDXHiSzuqG9/s72-c/aid72048-728px-Make-a-Voltage-Divider-Circuit-Step-6.jpg
Electrical for Us
https://www.sanjaysah.com.np/2016/12/electric-current-and-voltage-division.html
https://www.sanjaysah.com.np/
http://www.sanjaysah.com.np/
http://www.sanjaysah.com.np/2016/12/electric-current-and-voltage-division.html
true
3851448774078769448
UTF-8
Loaded All Posts Not found any posts VIEW ALL Readmore Reply Cancel reply Delete By Home PAGES POSTS View All RECOMMENDED FOR YOU LABEL ARCHIVE SEARCH ALL POSTS Not found any post match with your request Back Home Sunday Monday Tuesday Wednesday Thursday Friday Saturday Sun Mon Tue Wed Thu Fri Sat January February March April May June July August September October November December Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec just now 1 minute ago $$1$$ minutes ago 1 hour ago $$1$$ hours ago Yesterday $$1$$ days ago $$1$$ weeks ago more than 5 weeks ago Followers Follow THIS CONTENT IS PREMIUM Please share to unlock Copy All Code Select All Code All codes were copied to your clipboard Can not copy the codes / texts, please press [CTRL]+[C] (or CMD+C with Mac) to copy