Resistors in series and in parallel (review) Example R1 R1 R2 R2 r r

10. Kirchhoff’s rules Kirchhoff's first rule (Junction or current rule) Follows from the conservation of charges Example: I2 I1 I1=I2+I3 I3

2) Kirchhoff’s second rule (Loop or voltage rule) Follows from the conservation of energy R1 R2 R3 I V 3) Using Kirchhoff’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. ε2 R1 I1 I3 I2 ε1 R2 R3 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 loops We can use 2 equations

I3 flows opposite to our assumption Example 1 (continued) 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 We have three equations for three unknowns, we can solve this system of equations. Let us use numbers: I3 flows opposite to our assumption

Example 2: R1 I1 R2 I2 I3 R 9V 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

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

Example: A copper wire 2. 0 mm in diameter, caries 1. 0 A 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.