Fundamental Physics/Electricity/Electric Conductor

Electricity And Matter

Matter that interacts with electricity are divided into three types Conductor, Semi Conductor, and Non Conductor

• Conductor . All matter allow current to flow easily like Metal Ferrite, Copper
• Semi Conductor . All matter does not allow current to flow easily like Semi Conductor Silicon, Germanium
• Non Conductor . All matter does not allow current to flow like Rubber

Electric Conductor

Resistor

Resistor is a electric component thats exhibit resistance to the current flow . Resistance has a symbol R measured in ohm unit Ω .

Resistor is made from straight wire line conductor

${\displaystyle R=\rho {\frac {l}{A}}}$

DC Circuit Response From ohm's law

${\displaystyle V=IR}$
${\displaystyle R={\frac {V}{I}}}$
${\displaystyle I={\frac {V}{R}}}$

From Watt's law

${\displaystyle P=IV=I(IR)=I^{2}R}$

AC Response Circuit Impedance , Resistance to the AC current flow

${\displaystyle Z_{R}=R+X_{R}=R+0=R}$

Current , Current flows through resistor

${\displaystyle i={\frac {v}{Z_{R}}}}$

Voltage, Voltage of the resistor

${\displaystyle v=iZ_{R}}$

Power, Power of the resistor

${\displaystyle p=iv=i(iZ_{R})=i^{2}R}$

Capacitor

Capacitor in DC Circuit Capacitance has a symbol C measured in Farat unit F

Capacitance . ${\displaystyle C={\frac {V}{Q}}}$
Charge . ${\displaystyle Q={\frac {V}{C}}}$
Current . ${\displaystyle I={\frac {Q}{t}}}$
Voltage . ${\displaystyle V={\frac {W}{Q}}}$
Power . ${\displaystyle P_{C}=IV={\frac {Q}{t}}{\frac {W}{Q}}={\frac {W}{t}}}$
Voltage . ${\displaystyle v_{C}={\frac {1}{C}}\int idt}$
Current . ${\displaystyle i_{C}=C{\frac {dv}{dt}}}$
Reactance . Resistance to the AC current flow
In time domain
${\displaystyle X_{C}={\frac {v_{C}}{i_{C}}}}$
In frequency domain
${\displaystyle X_{C}(j\omega )={\frac {1}{j\omega C}}}$
In phasor domain
${\displaystyle X_{C}(\theta )={\frac {1}{\omega C}}\angle -90}$
Impedance . Resistance to the AC current flow
In time domain . ${\displaystyle Z_{C}=R_{C}+X_{C}}$
In frequency domain
${\displaystyle Z_{C}=R_{C}+{\frac {1}{j\omega C}}}$
${\displaystyle Z_{C}={\frac {j\omega T+1}{j\omega C}}}$
In phasor domain
${\displaystyle Z_{C}=R_{C}\angle 0+{\frac {1}{\omega C}}\angle -90}$
${\displaystyle Z_{C}={\sqrt {R_{C}^{2}+({\frac {1}{\omega T}})^{2}}}\angle -{\frac {1}{\omega T}}}$
Time Constant
${\displaystyle T=CR_{C}}$
Power . Power of the capacitor
${\displaystyle p={\frac {1}{2}}Cv_{C}^{2}}$

Inductor

Inductor in DC Circuit Inductance . Inductance has a symbol L measured in Henry unit H

${\displaystyle L={\frac {B}{I}}}$

Magnetic Intensity . Measurement of magnetic strength

${\displaystyle B=LI}$

Current

${\displaystyle I={\frac {B}{L}}}$

Voltage . ${\displaystyle v_{L}=L{\frac {di_{L}}{dt}}}$

Current . ${\displaystyle i_{L}={\frac {1}{L}}\int {dv_{L}}{dt}}$

Reactance . Resistance to the AC current flow

${\displaystyle X_{C}={\frac {v_{L}}{i_{L}}}}$
In frequency domain
${\displaystyle X_{L}(j\omega )=j\omega L}$
In phasor domain
${\displaystyle X_{L}(\omega \theta )=\omega L\angle 90}$

Impedance . Resistance to the AC current flow

${\displaystyle Z_{L}=R_{L}+X_{L}}$
In frequency domain
${\displaystyle Z_{L}=R_{L}+j\omega L}$

In phasor domain
${\displaystyle Z_{L}=R_{L}\angle 0+j\omega L\angle 90}$
${\displaystyle Z_{L}={\sqrt {R_{L}^{2}+(j\omega L)^{2}}}\angle \omega T}$

Time Constant

${\displaystyle T={\frac {L}{R_{L}}}}$

Power . Power of the capacitor

${\displaystyle p={\frac {1}{2}}Li^{2}}$

Electric Semi Conductor

Semi conductors like Si, Ge normally very low in conducting electricity . But if they are doped with impurity, they become doped negative or positive semi conductor which are easy to conduct electricity

Semi conductor + impurity --> [N] typed Semi conductor] or [P] typed Semi conductor]

Diode

A device made from joining one negative typed semi conductor with one positive typed semi conductor

- o--[N|P]--o +

Diode's circuit sysmbol

The IV chracteristic of diode is specified in IV Graph

As seen in the graph above the diode actually works in both the forward region and the backward region. In the forward region the value of I and V are positive and in the backward region I and V are negative.

Diode does not conduct current or turned OFF at ${\displaystyle V=V_{d}}$ of ${\displaystyle I=0}$
Diode starts to conduct current or turned ON at ${\displaystyle V=V_{d}}$ of ${\displaystyle I=1mA}$
Diode conducts current at ${\displaystyle V>V_{d}}$ at ${\displaystyle I=I_{o}[e^{({\frac {V_{d}}{nV_{T}}})t}-1]}$

Transistor

 Transistor Symbol Construction NPN transistor o-- [N P N] --o PNP transistor o-- [P N P] --o

Manufacturer's IV Graph specification tell transistor operation

${\displaystyle V . Transistor is OFF
${\displaystyle V=V_{d}.I=1mA}$ . Transistor is ON
${\displaystyle V>V_{d}.I=I_{o}e^{\frac {V}{V_{d}}}}$
${\displaystyle V=V_{S}.I=I_{s}}$ . Transistor is saturated

With the right connection, by connecting transistor with resistor(s) Transistor can acts as

${\displaystyle i_{b}>0}$
${\displaystyle i_{e}>\alpha i_{b}}$
${\displaystyle i_{c}>\beta i_{b}}$

Provided that, transistor should be turned ON with biased voltage at the base must be greater than diode's break over voltage

${\displaystyle v_{b}>v_{be}}$ . ${\displaystyle v_{be}=v_{d}}$
Transistor is switch On when ${\displaystyle V_{b}>V_{be}}$
Transistor is switch Off when ${\displaystyle V_{b}