Kirchhoff’s LawsKirchhoff’s LawsCurrent Law: The total current entering a junction Current Law: The total current entering a junction in a circuit equals the total current leaving.in a circuit equals the total current leaving.

I1 = 2A

I2 = ?

I3 = 5A

1 2 3I I I

Kirchhoff’s LawsKirchhoff’s Laws

Voltage Law: The total of all the potential Voltage Law: The total of all the potential differences around a closed loop in a circuit is differences around a closed loop in a circuit is zerozero

V1

V3

V2

Kirchhoff’s LawsKirchhoff’s Laws

For voltage sources:For voltage sources: Going from – to + represents a gain in energy Going from – to + represents a gain in energy

so potential difference is positiveso potential difference is positive Going from + to – represents a loss of energy Going from + to – represents a loss of energy

so potential difference is negativeso potential difference is negative

Kirchhoff’s LawsKirchhoff’s LawsFor resistors:For resistors: Passing in the same direction as the current Passing in the same direction as the current

represents a loss of energy -V=-(IR)represents a loss of energy -V=-(IR) Passing in the opposite direction to the Passing in the opposite direction to the

current represents a gain in energy +V=+(IR)current represents a gain in energy +V=+(IR)

Kirchhoff’s LawsKirchhoff’s LawsTo solve problems, To solve problems, follow a voltage loop follow a voltage loop around a circuit…around a circuit… a-ba-b b-cb-c c-dc-d d-ad-a

Then add up the p.d’s.Then add up the p.d’s.

V?

6V

4Ω

1Ω

a b

cd

2A

3A

Kirchhoff’s LawsKirchhoff’s LawsHarder….Harder…. a-ba-b b-cb-c c-dc-d d-ad-a Adding: Adding: So ISo I11

Using the current law:Using the current law:

4Ω

2Ω

8Ω

5V

V?

0.75A

I1?

I2?

a

b c

d

e f

Kirchhoff’s LawsKirchhoff’s Laws

Continued…Continued… b-cb-c c-fc-f f-ef-e e-be-b Adding:Adding:

4Ω

2Ω

8Ω

5V

V?

0.75A

I1?

I2?

a

b c

d

e f