(a) Determine the current supplied by the battery in the circuit as shown :

(b) Find currents in resistances `6 Omega` and `12 Omega`.

( c) Find values of `i, i_1, i_2` and `i_3`.

(d) Find current in `6 Omega` and potential difference between `A` and `B`
.

Explanation

(a) All resistances are in parallel
`(1)/(R_(eq)) = (1)/(24) + (1)/(12) +(1)/(24) + (1)/(12) = (1 + 2 + 1 + 2)/(24) = (6)/(24) =(1)/(4)`
`R_(eq) = 4 Omega`
Current supplied by battery `i= (24)/(4) = 6 A`

(b) `R_(eq) = 4 + 4 + 2 = 10 Omega`
Current supplied by battery `= (30)/(10) = 3 A`
`i_1 = (12)/(6 + 12) i = (2)/(3) xx 3 = 2 A`
`i_2 = i - i_1 = 3 - 2 = 1 A`
Or
`p.d`. across `X` and `Y`, `i xx 4 = 3 xx 4 = 12 V`
`p.d`. across `6 Omega` and `12 Omega` is also `12 V`
`i_1 = (12)/(6) = 2 A, i_2 = (12)/(12) = 1 A`

( c) Parallel,
`(1)/(R') = (1)/(8) + (1)/(12)+(1)/(24) = (3 + 2 + 1)/(24) = (1)/(4)`
`R' = 4 Omega`
`R_(eq) = 2 + 4 + 2 = 8 Omega`
`i = (48)/(8) = 6 A`
`p.d`. between `X` and `Y = 6 xx 4 = 24 V`
`i_1 = (24)/(8) = 3 A`
`i_1 = (24)/(12) = 2 A`
`i_3 = (24)/(24) = 1 A`.

(d) .