Introduction.
With connection in parallel, clams of generators & receivers are connected as on image #1. Thus all of clams connected in parallel are powered by the same voltage. Every of two-terminal circuits can be connected or disconnected independently of others.
(TODO: add image #1).
(... unfinished article, to be continued).
Showing posts with label Simple. Show all posts
Showing posts with label Simple. Show all posts
Thursday, December 31, 2015
Thursday, November 19, 2015
Simple Circuits: Connected in Series.
Introduction.
With connection in series, active two-terminal circuits (for example: generators), or passive (for example: resistors), are connected one after another.
Image #1: Two resistors connected in a serie.
Qualities of Connection in Series.
If we connect two resistors with connection in series to a power generator, the result of reading amperage before, in between & after resistors is always the same.
If we measure voltage on power generator's clams & on each of resitors as well, we'll notice that voltages on each of resistors are lesser than voltage of a power generator.
With a connection in series, on each of the resistors only part of voltage is lost. Whole voltage is spread across all of the resistors.
Sum of all voltages in a loop shown on Image #1, with direction considered, is totalling 0 (2nd Kirchoff's Law).
U - U2 - U1 = 0.
U = U1 + U2 + ...
This means that algebraic sum of all generators' voltages is equal to sum of all voltage losses on receivers.
If we measure (with ohmmeter) resistance of each of resistors & resistance of the whole circuit, we'll notice that resistance of whole circuit is equal to sum of resistances of each of resistors.
Current flowing through total resistance of whole circuit has the same intensity (amperage) as the current flowing through resistors connected in series.
R = R1 + R2 + ...
If individual resistors are equal, then with n resistors, total resistance is:
R = n · R1
On greater resistance there's greater voltage loss.
With connection in series, individual voltage drops are proportional to appropriate resistances.
U - generator's voltage;
U1, U2, ... - voltage drops;
R - total resistance;
R1, R2, ... - individual resistors;
Elements are connected in series when allowed voltage of individual element is smaller than generator's voltage.
Additional series-connected resistors.
Receiver (load) can be connected to a voltage greater than it's rated voltage if we add additional series-connected resistor(s). This resistor must be selected appropriately, to contain excess of a voltage & to survive the rated voltage of the generator.
Let's connect in series a light bulb 6V/0.3A with a generator with voltage of 24V. Let's use a resistor with appropriate resistance, to let it contain a voltage of 18V.
Image #2: A circuit with a resistor in a series-connection.
Voltage loss on leads.
In every circuit there are connected in series:
- power lead,
- receiver (load),
- return lead.
Because leads have a certain resistance Rl, with every receiver connection we have resistors connected in series.
Voltage loss on leads lowers receiver's (load's) voltage.
If we connect a light bulb to accumulator with a very long lead & if we measure voltage on a generator as well as a voltage on receiver (on load), we'll notice that a voltage on receiver (load) is lower than voltage on accumulator (generator). This is shown on image #3.
Image #3: A Practical Circuit, considering all of voltage losses.
If we'll connect in series to a first light bulb another a light bulb, voltage on receiver will be lower. Greater current's intensity (amperage) causes greater voltage loss in leads.
Voltage loss in leads is a cause for energy loss, that is transformed into heat. That's why it should be as small as possible. It's often given as a percentage of rated voltage.
Example #1:
Let's calculate a voltage loss in leads with a resistance of Rl = 2Ω connecting a light bulb 4,5V/1A with an accumulator.
ΔU = I · Rl = 1 A · 2 Ω = 2 V.
With connection in series, active two-terminal circuits (for example: generators), or passive (for example: resistors), are connected one after another.
Image #1: Two resistors connected in a serie.
Qualities of Connection in Series.
If we connect two resistors with connection in series to a power generator, the result of reading amperage before, in between & after resistors is always the same.
With connection in series, the amperage in each of two-terminal circuits is always the same. |
If we measure voltage on power generator's clams & on each of resitors as well, we'll notice that voltages on each of resistors are lesser than voltage of a power generator.
With a connection in series, on each of the resistors only part of voltage is lost. Whole voltage is spread across all of the resistors.
With connection in series, sum of voltage losses (voltage drops) in resistors is equal to power generator's voltage. |
Sum of all voltages in a loop shown on Image #1, with direction considered, is totalling 0 (2nd Kirchoff's Law).
This means that algebraic sum of all generators' voltages is equal to sum of all voltage losses on receivers.
If we measure (with ohmmeter) resistance of each of resistors & resistance of the whole circuit, we'll notice that resistance of whole circuit is equal to sum of resistances of each of resistors.
With connection in series, total resistance of whole circuit is equal to sum of individual resistances of each of particular resistors. |
Current flowing through total resistance of whole circuit has the same intensity (amperage) as the current flowing through resistors connected in series.
If individual resistors are equal, then with n resistors, total resistance is:
On greater resistance there's greater voltage loss.
With connection in series, individual voltage drops are proportional to appropriate resistances.
| U1 | R1 | U1 | R1 | |||
| = | = | |||||
| U | R | U2 | R2 |
U - generator's voltage;
U1, U2, ... - voltage drops;
R - total resistance;
R1, R2, ... - individual resistors;
Elements are connected in series when allowed voltage of individual element is smaller than generator's voltage.
Additional series-connected resistors.
Receiver (load) can be connected to a voltage greater than it's rated voltage if we add additional series-connected resistor(s). This resistor must be selected appropriately, to contain excess of a voltage & to survive the rated voltage of the generator.
Let's connect in series a light bulb 6V/0.3A with a generator with voltage of 24V. Let's use a resistor with appropriate resistance, to let it contain a voltage of 18V.
Image #2: A circuit with a resistor in a series-connection.
Voltage loss on leads.
In every circuit there are connected in series:
- power lead,
- receiver (load),
- return lead.
Because leads have a certain resistance Rl, with every receiver connection we have resistors connected in series.
Voltage loss on leads lowers receiver's (load's) voltage.
If we connect a light bulb to accumulator with a very long lead & if we measure voltage on a generator as well as a voltage on receiver (on load), we'll notice that a voltage on receiver (load) is lower than voltage on accumulator (generator). This is shown on image #3.
Image #3: A Practical Circuit, considering all of voltage losses.
ΔU = U1 - U2 | ΔU = I · Rl | |||
ΔU - voltage loss on leads. U1 - voltage loss on lead's beginning part. U2 - voltage loss on lead's ending part. I - current's intensity (amperage). Rl - lead's resistance. | ||||
On every lead through which the current flows, there's a voltage loss. |
If we'll connect in series to a first light bulb another a light bulb, voltage on receiver will be lower. Greater current's intensity (amperage) causes greater voltage loss in leads.
Voltage loss in leads is greater if the intensity (amperage) of the current is greater. Leads' greater resistance also causes greater voltage loss. |
Voltage loss in leads is a cause for energy loss, that is transformed into heat. That's why it should be as small as possible. It's often given as a percentage of rated voltage.
Example #1:
Let's calculate a voltage loss in leads with a resistance of Rl = 2Ω connecting a light bulb 4,5V/1A with an accumulator.
Wednesday, November 18, 2015
Simple Circuits: Arrow Notations.
Active & passive elements.
In electric circuits, there are active & passive elements:
- active element might be accumulator during power discharge,
- passive element might be accumulator during power charging.
Arrow notations.
Energy Flow.
On diagrams, arrows' directions mean positive direction of current's flow.
- positive current is the current flowing in direction of the positive flow, as noted with arrows,
- negative current is the current flowing in opposite direction of the positive flow, as noted with arrows.
Electric Current Arrow's Direction.
Reference arrow shows which of current's directions is positive. If electric current's direction & refernce arrow's direction are same, we have positive current. With opposite directions, we have negative current.
Voltage Arrow's Direction.
In a case of a voltage, reference arrows are drawn as arcs or straight lines that join points between which they show voltage.
Arrow's point shows positive voltage.
Two-Port Network with shown Electric Current's & Voltage's directions.
Direction of adding voltages can be shown by using indexes for voltage symbols. Positive direction of voltage is then counted starting from place marked by first-indexed symbol.
Two-Port Networks are energy converters that have two clamps at entering current side & two clamps at emerging current side. Current's arrows are drawn as to have them entering a Two-Port Network (it's marking system for a receiver device).
In electric circuits, there are active & passive elements:
- active element might be accumulator during power discharge,
- passive element might be accumulator during power charging.
Arrow notations.
Energy Flow.
On diagrams, arrows' directions mean positive direction of current's flow.
- positive current is the current flowing in direction of the positive flow, as noted with arrows,
- negative current is the current flowing in opposite direction of the positive flow, as noted with arrows.
Electric Current Arrow's Direction.
Reference arrow shows which of current's directions is positive. If electric current's direction & refernce arrow's direction are same, we have positive current. With opposite directions, we have negative current.
Voltage Arrow's Direction.
In a case of a voltage, reference arrows are drawn as arcs or straight lines that join points between which they show voltage.
Arrow's point shows positive voltage.
Two-Port Network with shown Electric Current's & Voltage's directions.
Direction of adding voltages can be shown by using indexes for voltage symbols. Positive direction of voltage is then counted starting from place marked by first-indexed symbol.
Two-Port Networks are energy converters that have two clamps at entering current side & two clamps at emerging current side. Current's arrows are drawn as to have them entering a Two-Port Network (it's marking system for a receiver device).
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