For a the current loops shown in the figu re, kirchhoff's loop rule for the loops AHDCBA and AHDEFGA yields these equations respectively.

Options

A. `-30I_(1)-41I_(3)+45=0` and ` -30I_(1)+21I_(2)-80=0`
B. `30I_(1)-41I_(3)+45=0` and ` 30I_(1)-21I_(2)-80=0`
C. `30I_(1)+41I_(3)-45=0` and `-30I_(1)+21I_(2)+80=0`
D. `-30I_(1)-41I_(3)-45=0` and `-30I_(1)+21I_(2)-80=0`

Answer

4

Explanation

Applying kirchhoff's loop rule for the closed loop
AHDCBA, we get
`-30l_(1)-45-40I_(3)=0`
`-30I_(1)-41I_(3)-45=0`
Applying kirchhoff's loop rule for the f closed loop
AHDEFGA, we get
`-30I_(1)+20I_(2)+I_(2)-80=0`
`-30I_(1)+21I_(2)-80=0`
None of the given options is correct
If the battery 45V is connected as the shown in the figure below, then option (a) is correct.

Applying kirchhoff's loop rule for the closed loop AHDCBA , we get
`-30I_(1)+45-I_(3)-40I_(3)=0`
`-30I_(1)-41I_(3)+45=0`
`-30I_(1)-41I_(3)+45=0`
Applying kirchhoff's loop law for the closed loop
AHDEFGA, we get
`-30I_(1)+20I_(2)+I_(2)80=0`
`-30I_(1)+21I_(2)-80=0`