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Question

For the combination of resistors shown in the following figure, find the equivalent resistance between M and N


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Solution

Step 1: Given data

Step 2: Formula used

For resistors in parallel combination

1RP=1R1+1R2+1R3+...+1Rn

Step 3: Finding the resultant resistances R3 and R4 which are connected in parallel

We know for resistors in parallel combination

1RP=1R1+1R2+1R3+...+1Rn

Since R3 and R4 are parallel, their resultant,

1R'=1R3+1R4R'=R3R4R3+R4

Step 4: Finding the resultant of all the four resistances R1,R2,R3 and R4

We know the resultant of resistances R3 and R4 is R'

Therefore the resultant of all four resistances R1,R2,R3 and R4 = The resultant of R1,R2 and R'

We know, for resistors in series combination:

RS=R1+R2+R3+...+Rn

Since R1,R2 and R' are connected in series, their resultant,

R=R1+R2+R'R=R1+R2+R3R4R3+R4

Therefore, the equivalent resistance between M and N is R1+R2+R3R4R3+R4.


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