1. Example
30k
We want to calculate the voltage Vac. To solve this problem the circuit can be redrawn as

2. I1
30k
Let the current I1 is flowing through the circuit. The KVL equation will be
10kI1 + 20kI1 + 30KI1 = 6
60kI1= 6

3. I1
30k I1 Vo
I1 = 6/60k
=0.1mA

4. Now Vac will be equal to Vac = (10k + 20k)I1 = 30k(0.1mA) =3 Volts. I1

5. Example
We want to calculate the voltage Vbd.
First we will have to calculate the voltage
across 40k resistor. Let the current I1 be
flowing through the loop.

6. Applying KVL
10kI kI1+ 10kI1 – 6=0
60kI1 = -3

7. I1 = - 3/60k
= mA

8. So, voltage across 40k resistor
V40k = (-0.05m)(40k)
= - 2 volts

9. Now to calculate Vbd we take the path
bdcb
Applying KVL
Vbd =0

10. d I1 e
40k
Vbd 2V + -
Vbd = 7 Volts.

11. Example
We want to calculate the current I0. The
circuit can be redrawn as

12. Here
I1 = 120 mA

13. Applying KVL to mesh 2 8kI2 + 4kI2 + 4k(I2 – I1 ) = 0
I2 = 480/16k =30 mA

14. I1 I2
4k
So I0 will be
I0 = I1 – I2
I0 = 120 – 30
= 90 mA

15. Example
We want to calculate the current I0 and
the voltage V0. The circuit can be redrawn as

16. V0
Applying KVL to mesh 1
2kI1 +6k(I1 – I2 )= 12
8kI1 – 6kI2 = 12

17. Applying KVL at mesh 2 8kI2 + 4kI2 + 6k (I2 – I1) = 0 18kI2 - 6kI1 =0

18. Solving equations of mesh 1 and 2 24kI1 - 18kI2 = 36

19. V0 I1 I2
I2 = 36/54k
=0.67mA

20. V0 I1 I2
Now V0 will be equal to
V0 = 4k I2
= 2.66 Volts

21. Example
We want to calculate the current I0. To
apply KVL the circuit can be redrawn as

22. Here
I1 = - 2mA
I3 = 4mA

23. KVL for mesh 2 4kI2 + 6k (I2 – I3) + 2k(I2 – I1) = 12
4mA
KVL for mesh 2
4kI2 + 6k (I2 – I3) + 2k(I2 – I1) = 12
12kI2 – =12

24. I0 I1 I2 I3
4mA
I2 = 32/12k
=8/3 mA
=2.66 mA
I0 = I2 = 2.66mA

25. Example
We want to calculate the current I0.The
circuit can be redrawn as

26. Here
I1 = - 2mA
I3 = 4mA

27. Apply KVL on the mesh 2 2kI2 + 1k(I2 – I1) = 12 3KI2 + 2 =12
I2 = 10/3 mA = 3.33mA

28. I0 I1 I3 I2
2k
Now
I0 = I1 – I2
= - 2 – 3.33
= mA