calculate the effective resistance between a and b
Answers
1. We have to find out equivalent resistance between A and B.
[ Refer fig 1 ]
➝ We have marked points C and D ( in fig 1).
➝ Now, first we will find out equivalent resistance between points A and C.
➝ Between points A and C , three resistors are connected in parallel connection. Therefore , equivalent resistance :-
=> 1/R' = 1+1+1
=> 1/R' = 3
=> R' = 1/3
Where ,R' = equivalent resistance
➝ Between points D and B , three resistors are connected in parallel connection. Therefore , equivalent resistance :-
=> 1/R' = 1+1+1
=> 1/R' = 3
=> R' = 1/3
➝ Now, we get three resistors in series combination with resistance 1/3 , 1 and 1/3 ohm. Now , their equivalent resistance :-
=>( 1/3)+( 1/3)+1
=> 5/3 ohm
Therefore, equivalent resistance = 3/5 ohm
____________________
2. We have to find out equivalent resistance between A and B.
[ Refer fig 2 ]
➝ We have marked points E,F,C and D ( in fig 2 ).
➝ Equivalent resistance between points C and D :-
=> R' = 3+3
=> R' = 6 ohm
➝ Equivalent resistance between points E and F :-
=> R' = 3+3
=> R' = 6 ohm
➝ Resistance of resistors of 6 ohm which are in parallel connection :-
=>1/ R' = (1/6)+(1/6)
=> 1/R' = 2/6
=>1/ R' = 1/3
=> R' = 3 ohm
Therefore, equivalent resistance = 3 ohm
_____________________
3. We have to find out equivalent resistance between A and B.
[ Refer fig 3 ]
➝ We have marked points C and D ( in fig 3 ).
➝ Equivalent resistance between points A and C :-
=> 1/ R' = (1/2)+(1/2)
=> 1/ R' = (2/2)
=> 1/ R' = 1
=> R' = 1 ohm
➝ Equivalent resistance between points C and D :-
=> 1/ R' = (1/2)+(1/2)
=> 1/ R' = (2/2)
=> 1/ R' = 1
=> R' = 1 ohm
➝ Equivalent resistance between points A and B :-
=> R' = 1+1+2 ( series combination )
=> R' = 4 ohm
Therefore, equivalent resistance = 4 ohm
