A Simple Guide to Kirchhoff’s Laws

Learning the basic rules of electric circuits!

Kirchhoff’s First Law: The Current Law (KCL)

The Big Idea: All the electricity that flows into a point must flow out of it.

In simple terms: Nothing gets lost! The amount of electric current going in is always equal to the amount coming out.

Analogy: Imagine a busy crossroads. The number of cars driving into the crossroads must equal the number of cars driving out of it. Electricity (current) works the same way at any connection point (node) in a circuit!

Rule: Current In = Current Out

KCL Examples (20 Examples)

Example 1: Find I_x

In: 2A

Out: 3A, I_x

2 = 3 + I_x

I_x = -1A (means 1A flows in)

Example 2: Find I_x

_x1A

In: 5A, 2A

Out: I_x, 1A

5 + 2 = I_x + 1

I_x = 6A

Example 3: Find I_a

_a4A3A

In: 10A, I_a, 4A

Out: 3A

10 + I_a + 4 = 3

I_a = -11A (11A flows out)

Example 4: Find I₁

₁7A12A

In: 12A

Out: I₁, 7A

12 = I₁ + 7

I₁ = 5A

Example 5: Find I_y

In: 6A

Out: 2A, I_y

6 = 2 + I_y

I_y = 4A

Example 6: Find I_z

In: 15A

Out: 8A, I_z

15 = 8 + I_z

I_z = 7A

Example 7: All currents leaving

In: 0

Out: 2A, 5A, I_x

0 = 2 + 5 + I_x

I_x = -7A (7A flows in)

Example 8: All currents entering

In: 3A, 4A, I_x

Out: 0

3 + 4 + I_x = 0

I_x = -7A (7A flows out)

Example 9: Find I_b

_b5A

In: 2A

Out: 1A, I_b, 5A

2 = 1 + I_b + 5

I_b = -4A (4A flows in)

Example 10: Find I_c

_c8A

In: 8A, 8A

Out: I_c

8 + 8 = I_c

I_c = 16A

Example 11: Find I_d

_d3A9A

In: I_d, 9A

Out: 3A

I_d + 9 = 3

I_d = -6A (6A flows out)

Example 12: Find I_e

_e12A

In: 12A

Out: I_e, 12A

12 = I_e + 12

I_e = 0A

Example 13: Find I_f

In: 2A, 3A

Out: 4A, I_f

2 + 3 = 4 + I_f

I_f = 1A

Example 14: Find I_g

_g5A5A

In: I_g

Out: 5A, 5A

I_g = 5 + 5

I_g = 10A

Example 15: Find I_h

In: 6A, 2A

Out: I_h

6 + 2 = I_h

I_h = 8A

Example 16: Find I_x

In: 5A

Out: I_x

5 = I_x

I_x = 5A

Example 17: Find I_x

In: 1A, I_x

Out: 0

1 + I_x = 0

I_x = -1A (1A flows out)

Example 18: Find I_x

_x3A3A

In: I_x

Out: 3A, 3A

I_x = 3 + 3

I_x = 6A

Example 19: Find I_x

_x7A

In: 10A

Out: 3A, I_x, 7A

10 = 3 + I_x + 7

I_x = 0A

Example 20: Find I_x

_x9A

In: I_x, 9A

Out: 4A

I_x + 9 = 4

I_x = -5A (5A flows out)

Kirchhoff’s Second Law: The Voltage Law (KVL)

The Big Idea: The energy you start with in a loop is the energy you end with.

In simple terms: In any complete circle (loop) in a circuit, the energy given by the battery must be completely used up by all the parts in that loop (like light bulbs or resistors).

Analogy: Think about climbing up a playground slide and then sliding down. You start on the ground. The ladder (like a battery) gives you “energy” to go up. When you slide down (like going through a light bulb), you use up that energy. By the time you reach the bottom, you’re back where you started with zero extra height. In a circuit loop, all the energy given must be used up!

Rule: Energy Gained = Energy Used

KVL Examples (20 Examples)

Example 21: Find V_R2

Gained: 12V

Used: 5V + V_R2

12V = 5V + V_R2

V_R2 = 7V

Example 22: Find V_S

_S=?R1=3VR2=6VR3=2V

Gained: V_S

Used: 3V + 6V + 2V

V_S = 11V

Example 23: Find V_R3

Gained: 24V

Used: 10V + 8V + V_R3

24V = 18V + V_R3

V_R3 = 6V

Example 24: Find V_R2

Loop: +20V – 8V + 5V – V_R2 = 0

17V – V_R2 = 0

V_R2 = 17V

Example 25: Find V_R1

Gained: 9V

Used: V_R1 + 4V

9V = V_R1 + 4V

V_R1 = 5V

Example 26: Find V_R1

Loop: +10V – V_R1 – 5V – 12V = 0

-7V – V_R1 = 0

V_R1 = -7V (polarity is backwards)

Example 27: Find V_S2

_S2=?R2=15V

Loop: +50V – 20V + V_S2 – 15V = 0

15V + V_S2 = 0

V_S2 = -15V

Example 28: Find V_R2

Gained: 18V

Used: V_R2 + 18V

18V = V_R2 + 18V

V_R2 = 0V

Example 29: Find V_S

_S=?R1=7VR2=3V

Gained: V_S

Used: 7V + 3V

V_S = 10V

Example 30: Find V_x

_xR3=15V

Gained: 40V

Used: 15V + V_x + 15V

40V = 30V + V_x

V_x = 10V

Example 31: Find V_S

_SR1=5VR2=5V

Gained: V_S

Used: 5V + 5V

V_S = 10V

Example 32: Find V_R3

Gained: 100V

Used: 25V + 50V + V_R3

100V = 75V + V_R3

V_R3 = 25V

Example 33: Find V_S1

_S1=?R1=12V–+3VR2=9V

Loop: +V_S1 – 12V + 3V – 9V = 0

V_S1 – 18V = 0

V_S1 = 18V

Example 34: Find V_R1

Loop: +15V – V_R1 – 5V – 5V = 0

5V – V_R1 = 0

V_R1 = 5V

Example 35: Find V_R2

Loop: -6V – 9V – V_R2 = 0

-15V – V_R2 = 0

V_R2 = -15V (polarity is backwards)

Example 36: Find V_R2

Gained: 10V

Used: 2V + V_R2

10V = 2V + V_R2

V_R2 = 8V

Example 37: Find V_S

_S=?R1=5VR2=15V

Gained: V_S

Used: 5V + 15V

V_S = 20V

Example 38: Find V_R3

Gained: 30V

Used: 10V + 10V + V_R3

30V = 20V + V_R3

V_R3 = 10V

Example 39: Find V_R1

Loop: +12V – V_R1 + 4V = 0

16V – V_R1 = 0

V_R1 = 16V

Example 40: Find V_S

_S=?R1=8VR2=4V

Gained: V_S

Used: 8V + 4V

V_S = 12V

Kirchhoff’s First Law: The Current Law (KCL)

KCL Examples (20 Examples)

Example 1: Find Ix

Example 2: Find Ix

Example 3: Find Ia

Example 4: Find I1

Example 5: Find Iy

Example 6: Find Iz

Example 7: All currents leaving

Example 8: All currents entering

Example 9: Find Ib

Example 10: Find Ic

Example 11: Find Id

Example 12: Find Ie

Example 13: Find If

Example 14: Find Ig

Example 15: Find Ih

Example 16: Find Ix

Example 17: Find Ix

Example 18: Find Ix

Example 19: Find Ix

Example 20: Find Ix

Kirchhoff’s Second Law: The Voltage Law (KVL)

KVL Examples (20 Examples)

Example 21: Find VR2

Example 22: Find VS

Example 23: Find VR3

Example 24: Find VR2

Example 25: Find VR1

Example 26: Find VR1

Example 27: Find VS2

Example 28: Find VR2

Example 29: Find VS

Example 30: Find Vx

Example 31: Find VS

Example 32: Find VR3

Example 33: Find VS1

Example 34: Find VR1

Example 35: Find VR2

Example 36: Find VR2

Example 37: Find VS

Example 38: Find VR3

Example 39: Find VR1

Example 40: Find VS

Example 1: Find I_x

Example 2: Find I_x

Example 3: Find I_a

Example 4: Find I₁

Example 5: Find I_y

Example 6: Find I_z

Example 9: Find I_b

Example 10: Find I_c

Example 11: Find I_d

Example 12: Find I_e

Example 13: Find I_f

Example 14: Find I_g

Example 15: Find I_h

Example 16: Find I_x

Example 17: Find I_x

Example 18: Find I_x

Example 19: Find I_x

Example 20: Find I_x

Example 21: Find V_R2

Example 22: Find V_S

Example 23: Find V_R3

Example 24: Find V_R2

Example 25: Find V_R1

Example 26: Find V_R1

Example 27: Find V_S2

Example 28: Find V_R2

Example 29: Find V_S

Example 30: Find V_x

Example 31: Find V_S

Example 32: Find V_R3

Example 33: Find V_S1

Example 34: Find V_R1

Example 35: Find V_R2

Example 36: Find V_R2

Example 37: Find V_S

Example 38: Find V_R3

Example 39: Find V_R1

Example 40: Find V_S