1. Calculating resistance
A variable cross-section resistor treated as a serial combination of small straight-wire resistors:

2. Example: Equivalent resistances

3. Series versus parallel connection
What about power delivered to each bulb?
What if one bulb burns out?

4. Symmetry considerations to calculate equivalent resistances
No current through the resistor I1 I2

5. To analyze more complex (steady-state) circuits:
Kirchhoff’s rules
To analyze more complex (steady-state) circuits:
For any junction: Sum of incoming currents equals to sum of outgoing currents
(conservation of charge)
Valid for any junction
2. For any closed circuit loop: Sum of the voltages across all elements of the loop is zero
(conservation of energy)
Valid for any close loop
- The number of independent equations will be equal to the number of unknown currents
Loop rule – statement that the electrostatic force is conservative.

6. Sign conventions for the loop rule

7. A single-loop circuit
Charging of a car battery

8. Complex networks
Find currents, potential differences and equivalent resistance

9. Electrical Measuring Instruments
Galvanometer
Can be calibrated to measure
current (or voltage)
Example: Full-scale deflection
Ifs =1 mA, internal coil resistance
Rc =20 W

10. For max current reading Ia of 50mA
For max voltage reading Vv =10V

11. Charging a Capacitor
(instantaneous application of Kirchhoff’s rules to non-steady-state situation)
Use lower case v, i, q to denote time-varying voltage, current and charge
Initial current
Final conditions, i=0

12. Time-constant When time is small, capacitor charges quickly.
For that either resistance or capacitance must be
small (in either case current flows “easier”)

13. Discharging a capacitor

14. Power distribution systems
Everything is connected in parallel
V=120 V (US and Canada)
V= V (Europe, Asia)

15. Circuit Overloads and Short Circuits
Fuse
Circuit breaker

16. Utility power (kW*h)

17. Magnetism First observation ~2500 years ago
in fragments of magnetized iron ore
Previously, interaction was thought
in terms of magnetic poles
The pole that points North on the magnetic
field of the Earth is called north pole
When points South – south pole
By analogy with electric field bar magnet
sets up a magnetic field in a space around it
Earth itself is a magnet. Compass needle
aligns itself along the earth’s magnetic field

18. Earth as a magnet

19. Magnetic Poles vs Electric Charge
The interaction between magnetic poles is similar to the Coulomb interaction of electric charges BUT magnetic poles always come in pairs (N and S), nobody has observed yet a single pole (monopole).
Despite numerous searches, no evidence of magnetic charges exist. In other words, there are no particles which create a radial magnetic field in the way an electric charge creates a radial field.

20. In turn, charged particles experience forces in those fields:
Magnetic Field
Lorentz force acting on charge q moving with velocity v in electric field E and magnetic field B
Electric charges produce electric fields E and, when move, magnetic fields B
In turn, charged particles experience forces in those fields:
For now we will concentrate on how magnetic force affects moving charged particles and current-carrying conductors…
Like electric field, magnetic field is a vector field, B