1. Resistors in series and in parallel (review) R1R1 R2R2 V1V1 V2V2 V I R1R1 I1I1 R2R2 I2I2 II R1R1 R2R2 r E r E R1R1 R2R2 Example

2. 10. Kirchhoff’s rules 1)Kirchhoffe’s first rule (Conservation of charges and junction or current rule) I1I1 I2I2 I2I2 Example I 1 =I 2 +I 3

3. 2) Kirchhoffe’s second rule (Loop or voltage rule) R1R1 R2R2 E1E1 E2E2 E3E3 E 4 <0 R3R3 I V 3) Using Kirchhoffe’s rules For N junctions write N-1 equations Write equations only for independent loops

4. Example 1: Determine the currents through the elements of this circuit. R1 R1 ε2ε2 R2 R2 R3 R3 I1I1 I2I2 I3I3 ε1ε1 We have 3 different currents We need 3 equations We have 2 junctions (N=2)We can use N-1=1 equation We have 2 independent loopsWe can use 2 equations

5. Junction equation: (Both junction give the same equation) Loop equations: If we add two equations above, we obtain the equation for the third (big, combined) loop. We do not need this equation – it is dependent from two previous Let us use numbers: I 3 flows opposite to our assumption Example 1 (continuation) An extra loop equation: We have three equations for three unknowns, we can solve this system of equations.

6. Example 2: E2E2 R1R1 R2R2 E1E1 I1I1 I2I2 I3I3 Example 3: In the circuit below, the switch is initially open. When the switch is closed, the current through the bottom resistor: R R 9 V A. IncreasesB. DecreasesC. Stays the same

7. 11. Microscopic picture L vdvd + For electrons in copper drift speed ~ 10 -5 - 10 -6 m/s Random-motion speed ~ 10 6 m/s A n – number of electric carriers per unit volume AL - volume

8. Example: A copper wire 2.0 mm in diameter, caries 1.0 A. What is the drift speed of electrons? Assume one electron per atom is free to move.