Find the equivalent resistance between AB AC and AD

Asked by megha.chhoti1456 | 2nd Aug, 2021, 08:53: PM

Expert Answer:

Let us name the resistors R, R2 ...................  R8  as shown in figure .
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Equivalent resistance between A and B :-
 
Resistors Rand R8 are redundant to get equivalent resistance between A and B .
Hence , they are removed in Step-1 as shown below
 
Now R, R5 and R7 are in series and equivalenet resistance of this series combination is 6 Ω .
Hence in step-2 , this series combination is replaced by 6 Ω resistor .
 
Now resistor R4 is in parallel with 6 Ω resistor,
Equivalenet resistance of parallel combination is  ( 2 × 6 ) / (2+6) = 1.5 Ω . 
 
Hence, finally, resistance between A and B is ( 2 + 1.5 + 2 ) = 5.5 Ω . 
 
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Equivalent resistance between A and C :-
 
Resistors Rand R8 are redundant to get equivalent resistance between A and C .
Hence , they are removed in Step-1 as shown below
 
Now R, R5 and R7 are in series and equivalenet resistance of this series combination is 6 Ω .
Hence in step-2 , this series combination is replaced by 6 Ω resistor .
 
Now resistor R2 is in parallel with 6 Ω resistor,
Equivalenet resistance of parallel combination is  ( 2 × 6 ) / (2+6) = 1.5 Ω . 
 
Hence, finally, resistance between A and C is ( 2 + 1.5 + 2 ) = 5.5 Ω . 
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Equivalent resistance between A and D :-
 
Resistors Rand R3 are redundant to get equivalent resistance between A and D .
Hence , they are removed in Step-1 as shown below
 
R2 and R5 are in series . Similarly R4 and R7 are in series .
 
Series combination of R2 and R5 , i.e., 4 Ω  is in parallel to series combination of R4 and R7 which is 4 Ω .
 
Hence two parallel 4 Ω resistors gives equivalenet resistance 2 Ω as shown in step-2 and step-3 .
 
Effective resistance between A and D is ( 2 + 2 + 2 ) Ω = 6 Ω
 

Answered by Thiyagarajan K | 2nd Aug, 2021, 11:54: PM