In the circuit shown in Fig. 5.79, determine the voltage drop between A and D.

Explanation

We need to divide this circuit inot three parts. We have left
loop, right loop, and the central part. To find out voltage drop
between points A and D, we have to apply Kirchhoff's second
law to these circuits one by one.
Also let us assume that Curretn `I_1` flows in the left circuit in
the clockwise direciton and curretn`I_2` flows in the right circuit in the anticlockwise direction.
Direction of both th currents is decided by the battery
presnet in the circuit as current flows from positve to negative.

Applying Kirchhoff's second law to left loop, we get
`=-2I_1 -3l_1 + 10=0 or - 5I_1 =-10 or I_1 = 2A`
Now applying Kirchhoff's second law to right loop, we get
`4I_2 +6I_2 - 20 = 0 or 10I_2 =20 or I_2 =2A`
Applying the law between points A and D, we get
`V_A - 3I_1 + 4-4I_2 = V_D or V_A - V_D = 3I_1 + 4I_2 - 4`
Putting values of `I_1 and I_2` in the above expression, we get
`V_A -V_D = 3xx2+4xx2 -4 =6+8-4 =10V`