Capacitor

OHM Poin 3/23/2020 Comment

What is capacitor

Capacitor is an electronic component that stores electric charge. The capacitor is made of 2 close conductors (usually plates) that are separated by a dielectric material. The plates accumulate electric charge when connected to power source. One plate accumulates positive charge and the other plate accumulates negative charge.

The capacitance is the amount of electric charge that is stored in the capacitor at voltage of 1 Volt.

The capacitance is measured in units of Farad (F).

The capacitor disconnects current in direct current (DC) circuits and short circuit in alternating current (AC) circuits.

Capacitor pictures

Capacitor symbols

Capacitor
Polarized capacitor
Variable capacitor

Capacitance

The capacitance (C) of the capacitor is equal to the electric charge (Q) divided by the voltage (V):

$C=\frac{Q}{V}$

C is the capacitance in farad (F)

Q is the electric charge in coulombs (C), that is stored on the capacitor

V is the voltage between the capacitor's plates in volts (V)

Capacitance of plates capacitor

The capacitance (C) of the plates capacitor is equal to the permittivity (ε) times the plate area (A) divided by the gap or distance between the plates (d):

$C=\varepsilon \times \frac{A}{d}$

C is the capacitance of the capacitor, in farad (F).

ε is the permittivity of the capacitor's dialectic material, in farad per meter (F/m).

A is the area of the capacitor's plate in square meters (m²].

d is the distance between the capacitor's plates, in meters (m).

Capacitors in series

The total capacitance of capacitors in series, C1,C2,C3,.. :

$\frac{1}{C_{Total}}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}+...$

Capacitors in parallel

The total capacitance of capacitors in parallel, C1,C2,C3,.. :

C_Total = C₁+C₂+C₃+...

Capacitor's current

The capacitor's momentary current i_c(t) is equal to the capacitance of the capacitor,

times the derivative of the momentary capacitor's voltage v_c(t):

$i_c(t)=C\frac{dv_c(t)}{dt}$

Capacitor's voltage

The capacitor's momentary voltage v_c(t) is equal to the initial voltage of the capacitor,

plus 1/C times the integral of the momentary capacitor's current i_c(t) over time t:

$v_c(t)=v_c(0)+\frac{1}{C}\int_{0}^{t}i_c(\tau)d\tau$

Energy of capacitor

The capacitor's stored energy E_C in joules (J) is equal to the capacitance C in farad (F)

times the square capacitor's voltage V_C in volts (V) divided by 2:

E_C = C × V_C²/ 2

AC circuits

Angular frequency

ω = 2π f

ω - angular velocity measured in radians per second (rad/s)

f - frequency measured in hertz (Hz).

Capacitor's reactance

$X_C = -\frac{1}{\omega C}$

Capacitor's impedance

Cartesian form:

$Z_C = jX_C = -j\frac{1}{\omega C}$

Polar form:

Z_C = X_C∟-90º

Capacitor types

Variable capacitor	Variable capacitor has changeable capacitance
Electrolytic capacitor	Electrolytic capacitors are used when high capacitance is needed. Most of the electrolytic capacitors are polarized
Spherical capacitor	Spherical capacitor has a sphere shape
Power capacitor	Power capacitors are used in high voltage power systems.
Ceramic capacitor	Ceramic capacitor has ceramic dielectric material. Has high voltage functionality.
Tantalum capacitor	Tantalum oxide dielectric material. Has high capacitance
Mica capacitor	High accuracy capacitors
Paper capacitor	Paper dielectric material

Resistor

OHM Poin 3/22/2020 Comment

What is Resistor

Resistor is an electrical component that reduces the electric current.

The resistor's ability to reduce the current is called resistance and is measured in units of ohms (symbol: Ω).

If we make an analogy to water flow through pipes, the resistor is a thin pipe that reduces the water flow.

Ohm's law

The resistor's current I in amps (A) is equal to the resistor's voltage V in volts (V)

divided by the resistance R in ohms (Ω):

The resistor's power consumption P in watts (W) is equal to the resistor's current I in amps (A)

times the resistor's voltage V in volts (V):

P = I × V

The resistor's power consumption P in watts (W) is equal to the square value of the resistor's current I in amps (A)

times the resistor's resistance R in ohms (Ω):

P = I² × R

The resistor's power consumption P in watts (W) is equal to the square value of the resistor's voltage V in volts (V)

divided by the resistor's resistance R in ohms (Ω):

P = V²/ R

Resistors in parallel

The total equivalent resistance of resistors in parallel R_Total is given by:

So when you add resistors in parallel, the total resistance is decreased.

Resistors in series

The total equivalent resistance of resistors in series R_totalis the sum of the resistance values:

R_total = R₁+ R₂+ R₃+...

So when you add resistors in series, the total resistance is increased.

Dimensions and material affects

The resistance R in ohms (Ω) of a resistor is equal to the resistivity ρ in ohm-meters (Ω∙m) times the resistor's length l in meters (m) divided by the resistor's cross sectional area A in square meters (m²):

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

Resistor image

Resistor symbols

	Resistor (IEEE)	Resistor reduces the current flow.
	Resistor (IEC)	Resistor reduces the current flow.
	Potentiometer (IEEE)	Adjustable resistor - has 3 terminals.
	Potentiometer (IEC)	Adjustable resistor - has 3 terminals.
	Variable Resistor / Rheostat (IEEE)	Adjustable resistor - has 2 terminals.
	Variable Resistor / Rheostat (IEC)	Adjustable resistor - has 2 terminals.
	Trimmer Resistor	Presest resistor
	Thermistor	Thermal resistor - change resistance when temperature changes
	Photoresistor / Light dependent resistor (LDR)	Changes resistance according to light

Resistor color code

The resistance of the resistor and its tolerance are marked on the resistor with color code bands that denotes the resistance value.

There are 3 types of color codes:

4 bands: digit, digit , multiplier, tolerance.
5 bands: digit, digit, digit , multiplier, tolerance.
6 bands: digit, digit, digit , multiplier, tolerance, temperature coefficient.

Resistance calculation of 4 bands resistor

R = (10×digit₁+ digit₂) × multiplier

Resistance calculation of 5 or 6 bands resistor

R = (100×digit₁+ 10×digit₂+digit₃) × multiplier

Resistor types

Variable resistor	Variable resistor has an adjustable resistance (2 terminals)
Potentiometer	Potentiometer has an adjustable resistance (3 terminals)
Photo-resistor	Reduces resistance when exposed to light
Power resistor	Power resistor is used for high power circuits and has large dimensions.
Surface mount (SMT/SMD) resistor	SMT/SMD resistors have small dimensions. The resistors are surface mounted on the printed circuit board (PCB), this method is fast and requires small board area.
Resistor network	Resistor network is a chip that contains several resistors with similar or different values.
Carbon resistor
Chip resistor
Metal-oxide resistor
Ceramic resistor

Pull-up resistor

In digital circuits, pull-up resistor is a regular resistor that is connected to the high voltage supply (e.g +5V or +12V) and sets the input or output level of a device to '1'.

The pull-up resistor set the level to '1' when the input / output is disconnected. When the input / output is connected, the level is determined by the device and overrides the pull-up resistor.

Pull-down resistor

In digital circuits, pull-down resistor is a regular resistor that is connected to the ground (0V) and sets the input or output level of a device to ' 0 '.

The pull-down resistor set the level to ' 0 ' when the input / output is disconnected. When the input / output is connected, the level is determined by the device and overrides the pull-down resistor.

Electrical Units

OHM Poin 3/22/2020 Comment

Electrical Units

Electrical & electronic units of electric current, voltage, power, resistance, capacitance, inductance, electric charge, electric field, magnetic flux, frequency:

Electrical & electronic units table
Units prefix table
Electrical units definitions

Electrical & electronic units table

Unit Name	Unit Symbol	Quantity
Ampere (amp)	A	Electric current (I)
Volt	V	Voltage (V, E) Electromotive force (E) Potential difference (Δφ)
Ohm	Ω	Resistance (R)
Watt	W	Electric power (P)
Decibel-milliwatt	dBm	Electric power (P)
Decibel-Watt	dBW	Electric power (P)
Volt-Ampere-Reactive	var	Reactive power (Q)
Volt-Ampere	VA	Apparent power (S)
Farad	F	Capacitance (C)
Henry	H	Inductance (L)
siemens / mho	S	Conductance (G) Admittance (Y)
Coulomb	C	Electric charge (Q)
Ampere-hour	Ah	Electric charge (Q)
Joule	J	Energy (E)
Kilowatt-hour	kWh	Energy (E)
Electron-volt	eV	Energy (E)
Ohm-meter	Ω∙m	Resistivity (ρ)
siemens per meter	S/m	Conductivity (σ)
Volts per meter	V/m	Electric field (E)
Newtons per coulomb	N/C	Electric field (E)
Volt-meter	V⋅m	Electric flux (Φ_e)
Tesla	T	Magnetic field (B)
Gauss	G	Magnetic field (B)
Weber	Wb	Magnetic flux (Φ_m)
Hertz	Hz	Frequency (f)
Seconds	s	Time (t)
Meter / metre	m	Length (l)
Square-meter	m²	Area (A)
Decibel	dB
Parts per million	ppm

Units prefix table

Prefix	Prefix Symbol	Prefix factor	Example
pico	p	10^-12	1pF = 10^-12F
nano	n	10^-9	1nF = 10^-9F
micro	μ	10^-6	1μA = 10^-6A
milli	m	10^-3	1mA = 10^-3A
kilo	k	10³	1kΩ = 1000Ω
mega	M	10⁶	1MHz = 10⁶Hz
giga	G	10⁹	1GHz = 10⁹Hz

Electrical units definitions

Volt (V)

Volt is the electrical unit of voltage.

One volt is the energy of 1 joule that is consumed when electric charge of 1 coulomb flows in the circuit.

1V = 1J / 1C

Ampere (A)

Ampere is the electrical unit of electrical current. It measures the amount of electrical charge that flows in an electrical circuit per 1 second.

1A = 1C / 1s

Ohm (Ω)

Ohm is the electrical unit of resistance.

1Ω = 1V / 1A

Watt (W)

Watt is the electrical unit of electric power. It measures the rate of consumed energy.

1W = 1J / 1s

1W = 1V ⋅ 1A

Decibel-milliwatt (dBm)

Decibel-milliwatt or dBm is a unit of electric power, measured with logarithmic scale referenced to 1mW.

10dBm = 10 ⋅ log₁₀(10mW / 1mW)

Decibel-Watt (dBW)

Decibel-watt or dBW is a unit of electric power, measured with logarithmic scale referenced to 1W.

10dBW = 10 ⋅ log₁₀(10W / 1W)

Farad (F)

Farad is the unit of capacitance. It represents the amount of electric charge in coulombs that is stored per 1 volt.

1F = 1C / 1V

Henry (H)

Henry is the unit of inductance.

1H = 1Wb / 1A

siemens (S)

siemens is the unit of conductance, which is the opposite of resistance.

1S = 1 / 1Ω

Coulomb (C)

Coulomb is the unit of electric charge.

1C = 6.238792×10¹⁸ electron charges

Ampere-hour (Ah)

Ampere-hour is a unit of electric charge.

One ampere-hour is the electric charge that flow in electrical circuit, when a current of 1 ampere is applied for 1 hour.

1Ah = 1A ⋅ 1hour

One ampere-hour is equal to 3600 coulombs.

1Ah = 3600C

Tesla (T)

Tesla is the unit of magnetic field.

1T = 1Wb / 1m²

Weber (Wb)

Weber is the unit of magnetic flux.

1Wb = 1V ⋅ 1s

Joule (J)

Joule is the unit of energy.

1J = 1 kg ⋅ m² / s²

Kilowatt-hour (kWh)

Kilowatt-hour is a unit of energy.

1kWh = 1kW ⋅ 1h = 1000W ⋅ 1h

Kilovolt-amps (kVA)

Kilovolt-amps is a unit of power.

1kVA = 1kV ⋅ 1A = 1000 ⋅ 1V ⋅ 1A

Hertz (Hz)

Hertz is the unit of frequency. It measures the number of cycles per second.

1 Hz = 1 cycles / s

Amps to Kilowatts Calculator

OHM Poin 3/21/2020 Comment

DC amps to kilowatts calculation

The power P in kilowatts (kW) is equal to the current I in amps (A), times the voltage V in volts (V) divided by 1000:

P(kW) = I(A) × V(V) / 1000

AC single phase amps to kilowatts calculation

The power P in kilowatts (kW) is equal to the power factor PF times the phase current I in amps (A), times the RMS voltage V in volts (V) divided by 1000:

P(kW) = PF × I(A) × V(V) / 1000

AC three phase amps to kilowatts calculation

Calculation with line to line voltage

The power P in kilowatts (kW) is equal to square root of 3 times the power factor PF times the phase current I in amps (A), times the line to line RMS voltage VL-L in volts (V) divided by 1000:

P(kW) = √3 × PF × I(A) × VL-L (V) / 1000

Calculation with line to neutral voltage

The power P in kilowatts (kW) is equal to 3 times the power factor PF times the phase current I in amps (A), times the line to neutral RMS voltage VL-N in volts (V) divided by 1000:

P(kW) = 3 × PF × I(A) × VL-N (V) / 1000

Typical power factor values

Do not use typical power factor values for accurate calculations.

Device	Typical power factor
Resistive load	1
Fluorescent lamp	0.95
Incandescent lamp	1
Induction motor full load	0.85
Induction motor no load	0.35
Resistive oven	1
Synchronous motor	0.9

Capacitor

What is capacitor

Capacitor pictures

Capacitor symbols

Capacitor

Polarized capacitor

Variable capacitor

Capacitance

Capacitance of plates capacitor

Capacitors in series

Capacitors in parallel

Capacitor's current

Capacitor's voltage

Energy of capacitor

AC circuits

Angular frequency

Capacitor's reactance

Capacitor's impedance

Capacitor types

Resistor

What is Resistor

Ohm's law

Resistors in parallel

Resistors in series

Dimensions and material affects

Resistor image

Resistor symbols

Resistor color code

Resistance calculation of 4 bands resistor

Resistance calculation of 5 or 6 bands resistor

Resistor types

Pull-up resistor

Pull-down resistor

Electrical Units

Electrical Units

Electrical & electronic units table

Units prefix table

Electrical units definitions

Volt (V)

Ampere (A)

Ohm (Ω)

Watt (W)

Decibel-milliwatt (dBm)

Decibel-Watt (dBW)

Farad (F)

Henry (H)

siemens (S)

Coulomb (C)

Ampere-hour (Ah)

Tesla (T)

Weber (Wb)

Joule (J)

Kilowatt-hour (kWh)

Kilovolt-amps (kVA)

Hertz (Hz)

Amps to Kilowatts Calculator

DC amps to kilowatts calculation

AC single phase amps to kilowatts calculation

AC three phase amps to kilowatts calculation

Calculation with line to line voltage

Calculation with line to neutral voltage

Typical power factor values

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