Find the equivalent resistance of the network between the point A and B shown in the figure . If A and B are connected to a 13 V battery so that `V_(A) gt V_(B)` . Find (a) the current in each resistor (b) the potential difference `V_(ab) = V_(a) - V_(b)` .

Explanation

For finding the equivalent resistance , let us connect the point A and B with a battery of emf V as shown in the figure . Suppose that the current supplied by the battery is i. Applying kirchhoff.s junction rule , let use distribute the current in different branches shown in the figure . Now , applying kirchhoff.s loop rule to the loop AcadB, we get
`1 i_(1) + 1(i_(1) - i_(2))= V `
` 2i_(1) - i_(2) = v " "......(i)`
Form the loop AcbdB, we get
`1 (i-i_(1)) + 2(i - i_(1) + i_(2)) = V`
or ` - 3i - 3i_(1) + 2i_(2) = V" " ..........(ii)`
From the loop AcabdB we get
`1 l_(1) + 1.i_(2) + 2(i-i_(1) + i_(2)) = V`
or ` 2i - i_(1) + 3l_(2) = V " ".....(iii)`
Eliminating `i_(2)` from the equation (i) and (ii) , we get
`3i + i_(1) = 3 " "......(iv)`
Eliminating `i_(2)` from equation (i) and (iii) , we get
` 2i + 5l_(1) = 4V " "......(V)`
Eliminating `i_(1)` from equation (iv) and (v) , we get
`13i = 11v`
`R_(eq) = (V)/(i) = (13)/(11) Omega" ".........(vi)`