Resistors in series and in parallel review I

Resistors in series and in parallel (review) I R 1 V 1 Example I 1 R 2 I V 2 V R 1 I I 2 R 1 R 2 E R 1 r E r R 2

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

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

Example 1: Determine the currents through the elements of this circuit. I 1 R 1 ε 2 I 3 I 2 ε 1 • We have 3 different currents • We have 2 junctions (N=2) • We have 2 independent loops R 2 R 3 We need 3 equations We can use N-1=1 equation We can use 2 equations

Example 1 (continuation) Junction equation: (Both junction give the same equation) Loop equations: An extra loop equation: 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: We have three equations for three unknowns, we can solve this system of equations. I 3 flows opposite to our assumption

Example 2: E 1 I 1 R 2 E 2 I 3 R Example 3: In the circuit below, the switch is initially open. When the switch is closed, the current through the bottom resistor: A. Increases B. Decreases C. Stays the same 9 V 9 V R

11. Microscopic picture L + vd A For electrons in copper drift speed ~ 10 -5 - 10 -6 m/s Random-motion speed ~ 106 m/s n – number of electric carriers per unit volume AL - volume

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.