(i) Calcuate the equivalent resistance of the given electronical network point A and B of

(ii) Also calculate the current through `ACB` if a `10 V` d.c source is connected between A and B and th e value of `R` is is assumed as `2 Omega`

Explanation

(i) The equivalent circuit is shown in fig. It is balanced Wheatstone bridge. So, the resistance connected between C and D is ineffective.
Resistance of arm ACD, `R_1=R+R=2R` , Resistance of arm ADB, `R_2=R+R=2R`
Equivalent resistance between A and B,
`R_(AB)` is given by `1/R_(AB)=1/(2R)+1/(2R)=2/(2R) implies R_(AB)=R=2Omega`
(ii) In arm CD, there is no current, `I_(cd)=0`
Current through arm ACD, `i_1=V/R_1`
`=10/(2R)=10/(2 times 2)=10/4=2.5A`