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

2. 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

3. 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

4. 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

5. 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

6. 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

7. vd 11. Microscopic picture AL - volume L For electrons in copper : A
drift speed ~ 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

8. 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.