1. 1 Electric Current Electric field exerts forces on charges inside it; Charges move under the influence of an electric field. The amount of charge moves through a cross section in unit time is defined as the electric current. For an electric field in vacuum, the moving charge can be either positive (ions) or negative (electrons). In a CRT tube (any of you still have those bulky old TV set?), the moving charge inside the CRT tube (vacuum) is electron. Often the electric field is “guided” by a conductor wire. What is flowing in the wire are the electrons, and they form the current. E V V V V

2. 2 Electric Current The direction of the current is defined as the direction of the moving positive charge, or, the direction of the electric field which always points from high potential to low potential. The unit of the electric current is Ampere in the SI system.  The ampere (Amp. or A) is an SI base unit.  Other SI base units are meter, kilogram (for mass), second, kelvin (for temperature), mole (quantity of matter) and candela (luminous intensity).  The definition of ampere: The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2·10 –7 Newton per meter of length.  Coulomb is defined through ampere as 1 coulomb = 1 ampere×1 second. Higher VLower V E

3. 3 Current density, Ohm’s Law and Conductivity For a given wire (conductor), the current normalized by the cross section represents the current density at that location: Cross section A current densitycurrent The derivation of this formula is easy and is left for you to work out.

4. 4 Current density, Ohm’s Law and Conductivity The motion of the electrons in a wire is the result of two forces: the acceleration of the electric field and the random scattering of the electron on the atoms. The actual average speed of the electrons is very slow: on the order of 10 -4 m/s. For a given wire, the scattering cross section is a constant (at a given temperature), the current density then should be proportional to the electric field (the acceleration force): Here σ is the proportional constant, called the conductivity of the given conductor. Since E is a vector, the current density j is also a vector. This is called the Ohm’s Law.

5. 5 Conductivity and resistivity When one closes a switch, what is applied to the apparatus is the electric field, not the actual electrons from the battery that delivers the electric energy to the apparatus. Example: However, the scattering of the electrons with the atoms in the wire does provide resistance to flow of the energy from the battery to the apparatus. This is the resistivity ρ. Since σ, the conductivity in j = σ E, is also a result of the electron atom scattering, σ and ρ must be related. Yes, indeed, and the formula is:

6. 6 Resistivity as a function of temperature For a given conductor, the resistance it represents to the current is proportional to the conductor’s length, inversely proportional to the conductor’s cross section. The proportional constant is the resistivity of this material: Empirical formula show that resistivity for most material follow a linear function of temperature: Where T 2 and T 1 are the temperatures. The α is temperature coefficient of resistivity. Another representation of this formula is:

7. 7 Ohm’s Law, a more commonly used format We used the word “resistance” in its sense in the English language. How do we actually define the resistance of a conductor to the current through it? This is defined as: the ratio of the potential difference across a conductor to the current through it. Translate into a formula: Sometimes written as: And this is called the Ohm’s Law. So one can think of Ohm’s Law as the definition of the resistance. Not all material relates the potential difference across it to the current through it the way that follows Ohm’s Law. Those that do follow Ohm’s Law are called Ohmic material. The device that is made from this type of material to resist current through it is called a resistor.

8. 8 Resistor Resistors are the most common passive component in a circuit. The other two passive components are the capacitor and the inductor. Resistors follow Ohm’s Law. The resistance a resistor presents to the current turns the electric potential energy into heat. The power consumed by a resistor (dissipated as heat) is P = V  I The power (P) the electric potential delivers equals to product of the potential difference (V) and the current (I). When the power is not turned into heat, (example: an electric motor), the above formula is still correct. Applying Ohm’s Law, we have: P = V  I = I 2  R = V 2 /R These formulas are only correct when a resistor is concerned.

9. 9 Example problems A lamp of 100W at 110V is connected with a cord of 0.75 meter long. The cord has a cross section of 1.5 mm 2, and is made of copper (ρ= 1.7 ×10 -8 Ωm). What is total resistance from the lamp and the cord? What is the heat dissipated through the cord when the lamp is turned on?

10. 10 Example problems If the rating of this cord is 15 A, can you use it to connect a 2000 W at 110V iron?

11. 11 Example problems

12. 12 Example problems

13. 13 Example problems You connected a 100W/110V light bulb to 220V, and a 100W/220V light bulb to 110V, what are the power consumptions you see from these light bulbs? Lamp1: 100W/110V, Lamp2: 110W/220V. FromP nominal = V 2 nominal /R, We haveR lamp1 = (110V) 2 /100W = 121Ω R lamp2 = (220V) 2 /100W = 484Ω When lamp1 is connected to 220V (do not try this at home!) P = V 2 /R = (220V) 2 /121 Ω = 400W When lamp2 is connected to 110V P = V 2 /R = (110V) 2 /484 Ω = 25W