1. As charges move through the circuit they loose their potential energy
Electromotive Force and Circuits
For a conductor to have a steady current, it must be a closed loop path
If charge goes around a complete circuit and returns to a starting point – potential energy does not change
As charges move through the circuit they loose their potential energy
due to resistance

2. “Electromotive force” (emf, ε) is produced by a battery or a generator and acts as a “charge pump”. It moves charges uphill and is equal to the potential difference across such a device under open-circuit conditions (no current). In reality, batteries have some internal resistance.
Emf is measured in Volts (so it is not a “force” per say, but potential difference)
Sources of emf – batteries, electric generators, solar cells, fuel cells

3. Evolution of the electric potential in the circuit with a load
Internal Resistance
In ideal situation,
Evolution of the electric potential in the circuit with a load
As the charge flows through the circuit, the potential
rise as it passes through the ideal source is equal to
potential drop via the resistance,

4. We measure voltages with voltmeters We measure currents with ammeters
An ideal voltmeter would have an infinite resistance
An ideal ammeter would have a zero resistance
Example: What are voltmeter
and ammeter readings?

5. Examples Bulb B is taken away, will the bulb A glow differently?
Which bulb glows brighter?
Which bulb glows brighter?

6. Potential gain in the battery
Potential changes around the circuit
Potential gain in the battery
Potential drop at all resistances
In an old, “used-up” battery emf is nearly the same, but internal resistance
increases enormously

7. Electrical energy and power
Chemical energy → Electric potential energy → Kinetic energy of charge carriers → Dissipation/Joule heat (heating the resistor through collisions with its atoms)
As the charge goes through the resistance the potential energy qV is expended (if both q and V are positive), but charge does not acquire kinetic energy (current is constant). Instead, it converted to heat. The opposite can also happen – if change in potential energy is positive, the charge acquires
it - battery

8. Power Output of a Source

9. Power Input to a Source Current flows “backwards”
Rate of conversion of electric energy
into non-electrical energy
Work is being done on, rather than by
the top battery (source of non-electrostatic
force)

10. Circuits in Series Resistance (light bulbs) on same path
Current has one pathway - same in every part of the circuit
Total resistance is sum of individual resistances along path
Current in circuit equal to voltage supplied divided by total resistance
Sum of voltages across each lamp equal to total voltage
One bulb burns out - circuit broken - other lamps will not light (think of string of old Christmas lights)

11. ISNS 3371 - Phenomena of Nature
Water Analogy for Series Circuits
ISNS Phenomena of Nature

12. Resistors in series

13. Parallel Circuits
Bulbs connected to same two points of electrical circuit
Voltage same across each bulb
Total current divides among the parallel branches - equals sum of current in each branch - current in each branch inversely proportional to resistance of branch
Overall resistance of circuit lowered with each additional branch
Household wiring (and new Christmas light strings) designed in parallel - too many electrical devices on - too much current - trip fuse/breaker

14. ISNS 3371 - Phenomena of Nature
Water Analogy for Parallel Circuits
ISNS Phenomena of Nature

15. Resistors in parallel

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

17. Example: Equivalent resistances

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

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

20. 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.