1. Kirchhoff’s Laws Current Law: The total current entering a junction in a circuit equals the total current leaving. I 1 = 2A I 2 = ? I 3 = 5A

2. Kirchhoff’s Laws Voltage Law: The total of all the potential differences around a closed loop in a circuit is zero V1V1 V3V3 V2V2

3. Kirchhoff’s Laws For voltage sources: Going from – to + represents a gain in energy so potential difference is positive Going from – to + represents a gain in energy so potential difference is positive Going from + to – represents a loss of energy so potential difference is negative Going from + to – represents a loss of energy so potential difference is negative

4. Kirchhoff’s Laws For resistors: Passing in the same direction as the current represents a loss of energy -V=-(IR) Passing in the same direction as the current represents a loss of energy -V=-(IR) Passing in the opposite direction to the current represents a gain in energy +V=+(IR) Passing in the opposite direction to the current represents a gain in energy +V=+(IR)

5. Kirchhoff’s Laws To solve problems, follow a voltage loop around a circuit… a-b a-b b-c b-c c-d c-d d-a d-a Then add up the p.d’s. V? 6V 4Ω4Ω 1Ω1Ω ab cd 2A 3A

6. Kirchhoff’s Laws Harder…. a-b a-b b-c b-c c-d c-d d-a d-a Adding: Adding: So I 1 So I 1 Using the current law: 4Ω4Ω 2Ω2Ω 8Ω8Ω 5V V? 0.75A I1?I1? I2?I2? a b c d e f

7. Kirchhoff’s Laws Continued… b-c b-c c-f c-f f-e f-e e-b e-b Adding: Adding: 4Ω4Ω 2Ω2Ω 8Ω8Ω 5V V? 0.75A I1?I1? I2?I2? a b c d e f