# 2 - Voltage, Current, Resistance and Power

##### 2016-04-18 18:45:00 +0000, 2 years and 4 months ago

2.01 - electricity basics

Electricity is the effect of movement of electrical charge.
The smallest quantity of electrical charge is one electron.

Voltage is a measure of how much energy the electronics in a circuit have.
Current is a measure of how many electrons are passing through a conductor.

There can only be a current (flow of electrons) in a component when there is a voltage across it. If there is no path for the electrons, there will be no current even though there may be a voltage difference.

Voltage = V, Volts, measured with a voltmeter, in parallel because it has ∞ resistance and would stop any current passing if it were in series.

           +---------+
+--+Voltmeter+--+   Voltmeter
|  +---------+  |   in parallel
^               v
|  +---------+  |
+-->-*--+Component+--*->--+
|+      +---------+       |
+--+---+                     |
+Supply+                     |
+--+---+                     |
|-                        |
+--<-------------------<--+


Current = A, Amps, measured with ammeter, in series because it has 0 resistance and so has no effect on the current, it must also be in series to measure how many electrons are passing through it.

           +---------+     +-------+
+--->---+Component+-->--+Ammeter+--+
|+      +---------+     +-------+  | Ammeter
+--+---+                              | in series
+Supply+                              |
+--+---+                              |
|-                                 |
+---<---------------<--------------+


2.02 - units

The most common units are:

QUANTITY UNIT SYMBOL
voltage volt V
current ampere A
resistance ohm
power watt W
frequency hert Hz

Each unit has a prefix, denoting how large the unit is, which makes them easy to say and write without having to say / write the entire number, these are:

prefix magnitude s.form units
giga x1,000,000,000 x10^9 GHz
mega x1,000,000 x10^6 MHz, MΩ
kilo x1,000 x10^3 kHz, kΩ, kV
UNIT x1 x1 Hz, Ω, V
milli x0.001 x10^-3 mV, mA, mW
micro x0.000 001 x10^-6 µV, µA, µF
nano x0.000 000 001 x10^-9 nF
pico x0.000 000 000 001 x10^-12 pF

Since most of these units aren’t used as their standard form, 1 Farad being the capacitance of the earth, and 1 Ohm being a very small resistance, it is necessary to change between the unit prefixes for convenience, this can be done easily using the following system:

 |->-*1000->-|
|           |
(G)iga--(M)ega--(k)ilo--UNIT--(m)illi--(µ)micro--(n)ano--(p)ico
|           |
|-<-/1000-<-|


In order to go to a higher prefix, nano to micro, all you have to do is multiply the unit that is the nano-x by 1000, and you’ll get the milli-x. As for going to a smaller unit prefix, divide the larger prefix for by 1000, and it gives the next lower prefix.

2.03 - Ohms law

This is the Ohms law equation, it can be rearranged to find Current and Resistance.

Electrons can move easily through some materials more than others. The aim of resistance is to make it harder for current to flow, thus reducing the total amount of power transferred in x time.
Resistance can be found by using:

Resistance is measured in Ohms (Ω).

2.04 - current in series and parallel circuits

Series circuits:
The below image is of two bulbs in series with each other, in a single, closed loop.

          +------+
+--->--+Bulb 1+-->--+
|+     +------+     | Bulbs
+--+---+               | in series
+Supply+               |
+--+---+               |
|-     +------+     |
+---<--+Bulb 2+--<--+
+------+


Current in a circuit is not ‘used up’ since it is the amount of electrons in a circuit, provided by the power supply, electrons cannot be generated or lost in a closed circuit.

Therefore the current value in amps at Bulb 1 is the same as the current value at Bulb 2.

Parallel circuits:
As explained in Kirchhoff’s current law:

“The total current into a node is equal to the total current flowing out of the same node.”

This behaviour can be explained in the following diagram:

         |                     \  |
v 0.2A            0.5A \ v 0.1A
|                       \|
---->----*---->----       ---<----*---->---
0.3A   node   0.5A        0.4A   node  0.2A

0.2A
+-----------+
+--+Component A+--+   Voltmeter
|  +-----------+  |   in parallel
^      0.4A       v
|  +-----------+  |
+-->-*--+Component B+--*->--+
|+      +-----------+       |
+--+---+                       |
+Supply+ @0.6A                 V 0.6A
+--+---+                       |
|-                          |
+--<-------------------<----+
0.6A


The arrows denote the direction of current
As shown in the image, even though the current is split at the node, it all comes back again at the last node to equal the full 0.6A, as outputted by the supply, therefore no current has been ‘used up’, because that is impossible.

2.05 - resistors in series

When several resistors are in series: \

• The same amount of current, (I) passes through each resistor.
• Vin is equal to the sum of the voltages across each resistor.
     +------+  +------+  +------+
+-->-+  R1  +--+  R2  +--+  R3  +->--+
|    +------+^ +------+^ +------+ ^  |
|            |         |          |  |
|      Vin   |         |          |  |
|       |   V1        V2         V3  |
|       |                            |
|       V   +------------+           |
+--<--------+ + Supply - +--------<--+
+------------+


Therefore, Vin can be found by adding the three voltages together:

Resistors in series can be added up to create, one, larger resistor:

    R1       R2       R3
+-----+  +-----+  +-----+
--+2.2k +--+3.4k +--+1.8k +- >--+
+-----+  +-----+  +-----+     |
|
--> R1 + R2 + R3              |
--> 2.2 + 3.4 + 1.8           V equal to
= 7.4kΩ                     |
|
+-----+                       |
--+7.4k +--                     |
+-----+                    <--+


2.06 - parallel circuits

Voltage in a parallel circuit is not shared, but current is, as shown in section 2.05.
As explained in Kirchhoff’s voltage law:

“The voltage gain at the supply is lost across the components in a circuit loop”

What this means is that all the voltage from Vin is used up, because voltage denotes energy (per coulomb of charge), and that energy is used in the circuit to create light, sound etc.

                8V
+-----------+
+--+Component A+--+   Voltmeter
|  +-----------+  |   in parallel
^       4V        V
|  +-----------+  |
+-->-*--+Component B+--*->--+
|+      +-----------+       |
+--+---+                       |
+Supply+ @12V                  V 0V
+--+---+                       |
|-                          |
+--<-------------------<----+
0V


As shown, the Supply voltage, +Vs is lost across both Component B and Component A, it is important to note that voltage is not split at the nodes, but voltage used by the component depends on the voltage draw. Indeed if the supply voltage exceeds the Component’s max voltage input, then it is most likely to overheat and fail.

2.08 - resistors in parallel

When two resistors are in parallel:

• The total current is equal to the separate currents of each resistor.
   +---->-------*----->---*
|            |         |
+--+---+       +++ R1    +++ R2
+Supply+@ 0.6A | | 0.3A  | | 0.3A
+--+---+       | |       | |
|           +++       +++
|            |         |
|            |         |
+----<-------*-----<---*  Assuming R1  R2


If two resistors are in parallel, then the total resistance can be calculated as:

           R1
+-----+
+Vs  +->-+15kΩ +->-+
|   +-----+   |
-->--*             *-->-- Rtotal
|   +-----+   |
+->-+10kΩ +->-+
+-----+
R2


When resistors are in parallel, the total resistance actually decreases, this is because there are more routes for the current to travel, thus reducing the overall effect of each individual resistor.

2.09 - resistors

A resistor is a component that restricts electrical current passing through it, a resistor is useful for providing a desired voltage across it when a current is passed through it.
The symbol for a resistor is:

There are three types of resistors:

• Carbon: Cheap, tend to be unstable, (tolerance changes with temperature) and can produce some unwanted noise.
• Metal oxide: More expensive, but have smaller tolerances which makes them more accurate stabler than carbon resistors and produce less electrical noise.
• Wire wound: The most expensive type of resistor but can be very accurate and stable.often designed to dissipate large amounts of power, they are seldom used in radio circuits because they have a appreciable inductance.

2.10 - resistor tolerance

Because of manufacturing, resistor values cannot be 100% accurate - the tolerance value shows how close in terms of resistance, that the resistor is to the actual value.
A resistor with a resistance of 100Ω and with a tolerance of 10%, has a possible resistance of 90 - 110Ω. Typical resistor tolerances are; 1%, 2%, 5%, 10% and 15%

2.11 - printed code

The BS1582 code, which is printed on various resistors, variable resistors and sometimes circuit diagrams consists of letters and numbers.

Where:

• R = x1
• k = x1,000
• M = x1,000,000

The position of the letter denotes the decimal point placement, as shown:

• 4R7 = 4.7Ω
• 4k7 = 4,700Ω
• 4M7 = 4,700,000Ω

The letter at the end denotes the tolerance:

• F = 1%
• G = 2%
• J = 5%
• K = 10%
• M = 20%

For example:

• 270RG = 270Ω 2%
• 47KJ = 47,000Ω 5%
• 1M5K = 1,500,000Ω 10%

2.12 - resistor colour codes

A resistor can have either 4 or 5 coloured bands paint around it.

The first two bands denote the first two significant figures, the third value denotes the multiplier and the fourth denotes the resistor tolerance.

The codes and their assigned colours are as follows:

COLOUR V.1 V.2 MULTIP. TOL.%
black 0 0 - 1%
brown 1 1 0 2%
red 2 2 00 -
orange 3 3 000 -
yellow 4 4 0000 -
green 5 5 00000 -
blue 6 6 000000 -
violet 7 7 - -
grey 8 8 - -
white 9 9 - -
silver - - 0.01 10%
gold - - 0.1 5%

For example: green, blue, red, gold 5 6 00 5% = 5.6kΩ 5%

yellow, violet, brown, gold 4 7 0 5% =470Ω 5%

2.13 - preferred values (E24 series)

Exact values are unnecessary in most circuits, only preferred values are made. The values chosen for the E24 series is as follows:
1.0, 1.1, 1.2, 1.5, 1.6, 1.8, 2.0, 2.2, 2.7, 3.0, 3.3, 3.6, 3.9, 4.3, 4.7, 5.1, 5.6, 6.2, 7.5, 8.2, 9.1
And every one of these that are powers of 10 greater.

These values give maximum coverage within minimum overlap with the 5% tolerance rating.

2.14 - heating and magnetic effects of electrical current

The amount of heat generated depends on:

• the resistance of the material
• the amount of current flowing

The strength of magnetic field is determined by how many electrons are forced to pass in the same direction, i.e. on the strength of the electrical current.

Therefore electrical current produced both a heating and magnetic effect.

2.15 - electrical power

Electrical power is given out (dissipated) by a component, it is the product of voltage across a component and the current through the component.

Ohm’s law states that V = I R
So substituting V in the power equation gives us:

Similarly:

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