Main ObjectiveWe now consider situations involving electric charges that are in

motion through some region of space

❑ Although the charges are discrete object,

they can still be considered as continuous variable

because number of charged particles under treatment is very large.

Instantaneous current

❑ The measurement of the

motion of charge carriers

is determined by

Current Density

𝑱 ≡𝑰

𝑨= 𝒏𝒒𝒗𝒅

𝑰 =𝟏

𝑹∆𝑽

𝑱 = 𝝈𝑬Ohm’s Law (Microscopic Definition)

Resistance and Resistors• The circuit elements that control the amount of current is called resistor.

• Resistance of a wire is given by

• 𝑅 ∶ 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒, 𝝆:𝑹𝒆𝒔𝒊𝒔𝒕𝒊𝒗𝒊𝒕𝒚, 𝑙: 𝑙𝑒𝑛𝑔𝑡ℎ, 𝐴: 𝑐𝑟𝑜𝑠𝑠 − 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎

𝑹 = 𝝆𝒍

𝑨

❑ The resistivity is the inverse of the conductivity 𝝆 = Τ𝟏 𝝈

Resistors Color Code

Ohmic vs Nonohmic Materials

❑ (a) The current–potential difference curve for an ohmic material.

The curve is linear, and the slope is equal to the inverse of the resistance of the

conductor.

❑ (b) A nonlinear current–potential difference curve for a junction diode.

This device does not obey Ohm’s law.

❑ The resistance of the conductor is too small when compared to the resistance of insulators

➢ Temperature dependency of

the resistivity of common conductors

➢ Temperature dependency of

the resistivity of superconductors

Comparison of the temperature dependencies of the resistivity of conductors and semiconductors

As temperature increases

• In conductors, the number of collisions between charges increases in conductor,

thus decreasing the drift speed

• In semiconductors, the number of charge carriers increases;

More electrons are available in the conduction band due to a decrease in the band gap

Power: Energy deliverance rate/ Energy per time

The current would double The power would be four times larger

0,0698𝑥35 ≈ 2,4 𝑘𝑟

In reality, the cost is higher because some energy is

transferred from the water into the surroundings by heat and

electromagnetic radiation while its temperature is

increasing.

• If you have electrical devices in your home with

power ratings on them, use this power rating and

an approximate time interval of use to estimate the

cost for one use of the device.