q3please help by explaining an solving

Question

Use Kirchhoff's laws to determine the current through the 15 ohm resistor in the bridge circuit shown in figure 2

Answer 1

Step 1:

Kirchoff's Current laws :

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

Kirchoff's Voltage laws :

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

Using kirchoff's current law :

At node B :

                                                (1)

At node C :

                                                (2)

Using kirchoff's voltage law :

Loop ABCA :

                              (3)

Loop BDCB :

                            (4)

Loop ACDA :

                                     (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 resistor is .