Electrical Engineering

Ohm's Law: Volts = Amps * Ohms That means that you have 45 volts across the resistor. Power = Volts * Amps That means that you 3.375 Watts going through the resistor.

Alternative Answer

Multiply the square of the current by the resistance.

Although we use the term 'Phase angle' it's also an angle referred to another phasor (voltage or current).

For example,

conventionally when expressing power factor, we use 'voltage' as the reference. So the 'phase angle' of a particular phasor is the phase difference between our reference (voltage) & the phasor.

As the gist, both mean the same except that 'phase angle' is the direction of the phasor w.r.t. positive x direction (reference)..

By definition, phase angle is the angle by which a load current leads or lags a supply voltage.

Phase difference is the angle between any two electical quantities -for example, the angle two phase voltages of a three-phase system.

Whenever a signal with components at several different frequencies flows through a diode,

the diode causes "mixing" among the frequencies ... for every pair of frequencies in the original

signal, two new frequency components are created: one at the sum of the original two, and one

at their difference. That is, if the original signal's wave has frequencies 'A' and 'B' in it, and it's

passed through a diode, then the output wave will have four frequencies in it: A, B, A+B, and A-B.

The original signal that enters an AM radio is the one that comes down from the antenna. If it's

an AM radio signal, then it consists of three frequencies: Carrier, Carrier+music, and Carrier-music.

There are 3 pairs of frequencies in this set. For each pair, the diode creates new signal components,

at the sum and difference of the original 2 frequencies. So with 3 different frequencies before the

diode, we have all of the following frequencies coming out after the diode:

1). Carrier

2). Carrier+music

3). (Carrier) + (Carrier+music)

4). (Carrier) - (Carrier+music)

5). Carrier

6). Carrier-music

7). (Carrier) + (Carrier-music)

8). (Carrier) - (Carrier-music)

9). Carrier+music

10). Carrier-music

11). (Carrier+music) + (Carrier-music)

12). (Carrier+music) - (Carrier-music)

To see what we've got now, let's go through the list and simplify the expressions:

1). Carrier

2). Carrier+music

3). 2xCarrier + music

4). -music

5). Carrier

6). Carrier-music

7). 2 x Carrier - music

8). music

9). Carrier+music

10). Carrier-music

11). 2 x Carrier

12). 2 x music

Looking through the list, we see that 9 of the 12 products are up around the frequency of the

radio carrier. It's easy to filter them out and throw them away, leaving only the following

three component signal frequencies, in the audio range:

4). -music

8). music

12). 2 x music

Mathematically, positive and negative frequencies are the same signal, so components #4 and #8

can be added to produce a component with double the amplitude (volume) of either one, which

only leaves the component at double the frequency of the music. It's in the range of legitimate

music frequencies, so we can't get rid of it completely. But it's weak to begin with, when it comes

out of the diode, and it's competing with the double-amplitude component at the real-music-frequency,

so it doesn't trash the desired signal too severely. What we're left with is the components

equal to the frequencies in the original music program, with some unavoidable distortion

on account of the presence of the low-level second harmonic.

The purpose of the diode was to perform the mixing of frequencies, so that we could separate

them by filtering, discard the ones that were used only to transport the music to us through

space, and keep the ones we want to send to the speaker or earphones.

Current Transformer- Instrument transformer used for measure high current. it has

less and thin turns in primary and more and thick turns in secondary.

Potential transformer- Instrument transformer used for measure high voltage. it has more and thin turns in primary and less and thick turns in secondary.

Unfortunately, the original answer has got things the wrong way around for the CT! A current transformer's primary has a thicker conductor than its secondary.

A pulse width modulation generator regulates the on and off times of a square wave-form.

It is commonly used in dimmer-switches and utilizes high frequency.

Example of waveform:

555555555555555554444444422222222111111110000000000000000

This waveform is 50% on and 50% off. In a light-bulb this would mean that you only get approximately 50% of the light it can give you. It is dimmed down 50%.

By modulating this waveform, we can get more or less light whilst keeping frequency the same.

Example:

555555555555555555555444444444222222222111111111000000000000

As you can see, the frequency is the same, but it is more on than off.

In this example, it is 75% on and 25% off, giving you 75% of maximum light.

Another example:

555555555555544444444222222221111111100000000000000000000

Here we have only 25% on and 75% off, yet still keeping the frequency the same.

Dimmer-switches can be made in a few different ways.

We can chop off parts of the sinusoidal waveform we get from the AC outlet.

This would be the same as regulating the pulse width of the sinus curve of AC Voltage.

We can regulate the voltage. This could be an approach of a battery-operated lamp.

The problem is that voltage regulation mean a lot of heat. (depending on method used.)

If regulating a 12 volt source down to 6 volt in order to dim a light bulb, 6 volt will go to the bulb and 6 volt will "burn up" in the regulator circuitry. If the bulb is 50 watt, then 25 watt will burn in the bulb, and the rest will create heat in the circuitry.

Now for the art of Pulse Width Modulation.

We make a generator that vary the pulse width instead of the voltage.

At 50 Hertz, we will hear the bulb hiss and we might notice some flicker.

At 5 Kilo Hertz, we will hear the bulb sing at a high pitch but the flicker is all gone.

At 25 Kilo Hertz, we might hear a very high frequency sound, but for most this is not noticeable.

(It is actually possible to make a light regulator that utilizes the bulb as a speaker to play music.)

At 35 Kilo Hertz, all audible noise is gone (although your dog might notice it)

By regulating the pulse width at 35 Khz we can dim the light up and down very accurately using Power MosFets'

A Power Mosfet has got the ability to switch electricity on and off in a fraction of a second. It has got very low internal resistance and very little power is consumed as heat. (Frequencies of 100Khz is easily obtainable and is often utilized.)

Advantages of PulseWidth Modulation:

Low power-consumption (little heat)

Small circuitry needed.

Extended battery life. Dim down 50% and your battery last almost 50% longer.

Disadvantages:

As the voltage rise and fall extremely rapidly, this creates an electromagnetic pulse. These pulses might interfere with electrical equipment like radio and TV (Not limited by these)

(By introducing a coil, we can eliminate much of this radio-noise.)

It is "difficult" to make a proper working circuitry able to dim fluorescent light.

A pulse width modulator for DC as in a battery can be made using very few components.

2 OpAmp

a couple of resistors.

a couple of capacitors.

1 PowerMosFet

1 Variable resistor (for adjusting the pulse width)

1 zener diode (3,3-5,6 Volt)

Cheap to make and long lasting.

No the SI base units are:

• metre for length
• kilogram for mass
• second for time
• ampere for electric current
• kelvin for temperature
• candela for luminous intensity
• mole for the amount of substance.

Voltage is derived from the base units, metre, kilogram, seconds and ampere.

V = m2·kg·s−3·A−1

Definition of voltage

The voltage between two ends of a path is the total energy required to move a small electric charge along that path, divided by the magnitude of the charge.

V = J/C

where:

J=m2·kg·s−2

C=s·A

V = (m2·kg·s−2)/(s·A)

Thus:

V = m2·kg·s−3·A−1

For more information look at the subject of "SI derived units"