Step 1:

Kirchoffs Current laws :

The sum of the currents flowing into and out of the node of a circuit is zero.

Kirchoffs Voltage laws :

The sum of the potential differences across the components forming a loop will be zero.

Using kirchoffs current law :

At node B :

                                                 (1)

At node C :

                                                 (2)

Using kirchoffs voltage law :

Loop ABC :

                           (3)

Loop BDC :

                         (4)

Loop ACD :

                                     (5)

Step 2:

Find by using above equations.

Substitute equation (1) and equation (5) in equation (3).

                (6)

Substitute equation (2) in equation (5).

                                    (7)

Substitute equation (7) in equation (6).

                      (8)

Substitute equation (7) and equation (8) in equation (4).

.

Here negative sign indicates direction of the current.

Solution :

The current through resistance is .