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 . ${\displaystyle P_{C}=IV={\frac {Q}{t}}{\frac {W}{Q}}={\frac {W}{t}}}$

Capacitor in AC Circuit

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

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

Inductor in AC Circuit

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

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

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

${\displaystyle V<V_{d}.I=0}$ . 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

An electronics amplifier

${\displaystyle i_{b}>0}$

${\displaystyle i_{e}>\alpha i_{b}}$

${\displaystyle i_{c}>\beta i_{b}}$

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

${\displaystyle v_{b}>v_{be}}$ . ${\displaystyle v_{be}=v_{d}}$

An electronics switch

Transistor is switch On when ${\displaystyle V_{b}>V_{be}}$

Transistor is switch Off when ${\displaystyle V_{b}<V_{be}}$