In the circuit shown in the circuit through

Options

A. the `3 Omega` resistor is `0.50A`
B. the `3 Omega` resistor is `0.25A`
C. the `4 Omega` resistor is `0.50A`
D. the `4 Omega` resistor is `0.25A`

Answer

d

Explanation

The current through the various branches of the circuit willl be

According to Kirchhoff's second law in closed circuit `CDEFC`
`2I_(2)+4I_(2)+ 2I_(2) - 8(I_(1)- I_(2)) = 0`
or `8 I_(1) = 16I_(2) or I_(1)= 2I_(2)`....(i)
In closed circuit `BCRFGB` ,
`2I_(2)+8(I_(1)- I_(2)) +2I_(2) - 8(I- I_(1)) = 0`
or `20 I_(1) - 8 I_(2)= 8I or 40 I_(2)- 8I_(2) = 8I`
or `l_(2)= l//4`....(ii)
From (i) `I_(1) = 2 xx I//4= I//2`
In a closed circuit `ABGHA`
`(3 I+8(I - I_(1))+2 I= 9`
or `9 = 13 I - 8 I_(1)= 13 I - 8(I//2) = 9 I or I = 1 A`
From (ii) `I_(2) = (1)/(4) = 0.25A`