RL Circuit - Revision history

Jiwym: /* References */

2015-12-06T01:52:23Z

References

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	6. http://www.intmath.com/differential-equations/5-rl-circuits.php		6. http://www.intmath.com/differential-equations/5-rl-circuits.php


	~~[[Category:Which Category did you place this in?]]~~

Jiwym at 01:51, 6 December 2015

2015-12-06T01:51:31Z

← Older revision		Revision as of 21:51, 5 December 2015
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	1. http://electricalstudy.sarutech.com/rl-circuit-transfer-function-time-constant-rl-circuit-as-filter/index.html		1. http://electricalstudy.sarutech.com/rl-circuit-transfer-function-time-constant-rl-circuit-as-filter/index.html

	2. http://powerdiscount.co.uk/ec36-lc502k-36w-magnetic-switch-start-choke-for-fluorescent-lamps-24050-ballast-990-p.asp		2. http://powerdiscount.co.uk/ec36-lc502k-36w-magnetic-switch-start-choke-for-fluorescent-lamps-24050-ballast-990-p.asp

	3. https://en.wikiversity.org/wiki/RL_Circuit		3. https://en.wikiversity.org/wiki/RL_Circuit

	4. http://www.electrical4u.com/rl-circuit-transfer-function-time-constant-rl-circuit-as-filter/		4. http://www.electrical4u.com/rl-circuit-transfer-function-time-constant-rl-circuit-as-filter/

	5. https://en.wikipedia.org/wiki/Fluorescent_lamp		5. https://en.wikipedia.org/wiki/Fluorescent_lamp

	6. http://www.intmath.com/differential-equations/5-rl-circuits.php		6. http://www.intmath.com/differential-equations/5-rl-circuits.php


	[[Category:Which Category did you place this in?]]		[[Category:Which Category did you place this in?]]

Jiwym at 01:50, 6 December 2015

2015-12-06T01:50:18Z

← Older revision		Revision as of 21:50, 5 December 2015
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	<math>\therefore t = 0.0550\: second</math>		<math>\therefore t = 0.0550\: second</math>

	~~==History==~~

	~~Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.~~		==References==

	~~== See also ==~~		1. http://electricalstudy.sarutech.com/rl-circuit-transfer-function-time-constant-rl-circuit-as-filter/index.html
			2. http://powerdiscount.co.uk/ec36-lc502k-36w-magnetic-switch-start-choke-for-fluorescent-lamps-24050-ballast-990-p.asp
	~~Are there related topics or categories in this~~ wiki ~~resource for the curious reader to explore? How does this topic fit into that context?~~		3. https://en.wikiversity.org/wiki/RL_Circuit
			4. http://www.electrical4u.com/rl-circuit-transfer-function-time-constant-rl-circuit-as-filter/
			5. https://en.wikipedia.org/wiki/Fluorescent_lamp
	~~==References==~~		6. http://www.intmath.com/differential-equations/5-rl-circuits.php

	~~This section contains the the references you used while writing this page~~

	[[Category:Which Category did you place this in?]]		[[Category:Which Category did you place this in?]]

Jiwym: /* Numerical */

2015-12-06T01:48:50Z

Numerical

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	===Numerical===		===Numerical===
	How much time is required for the RL circuit composed of one ~~1.5~~<math>V</math> battery, a resistor resistance of 0.5~~<math>~~\Omega</math> and an inductor with inductance of ~~0.03~~<math>H</math> to reach 60% of the maximum current?		How much time is required for the RL circuit composed of one <math>1.5V</math> battery, a resistor resistance of <math>0.5\Omega</math> and an inductor with inductance of <math>0.03H</math> to reach 60% of the maximum current?

	First, we find the maximum current.		First, we find the maximum current.

Jiwym: /* Examples */

2015-12-06T01:48:14Z

Examples

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	==Examples==		==Examples==

	===~~Simple~~===		===Theoretical===
	After the steady state has been reached and the current has reached its maximum value, you attempt to open the circuit. In the short period of time when you open the circuit, what would you expect to happen?		After the steady state has been reached and the current has reached its maximum value, you attempt to open the circuit. In the short period of time when you open the circuit, what would you expect to happen?

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	===~~Middling~~===		===Numerical===
	How much time is required for the RL circuit composed of one 1.5<math>V</math> battery, a resistor resistance of 0.5<math>\Omega</math> and an inductor with inductance of 0.03<math>H</math> to reach 60% of the maximum current?		How much time is required for the RL circuit composed of one 1.5<math>V</math> battery, a resistor resistance of 0.5<math>\Omega</math> and an inductor with inductance of 0.03<math>H</math> to reach 60% of the maximum current?

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	<math>\therefore t = 0.0550\: second</math>		<math>\therefore t = 0.0550\: second</math>

	~~<math></math>~~
	~~<math></math>~~
	~~===Difficult===~~

	==History==		==History==

Jiwym: /* Examples */

2015-12-06T01:35:12Z

Examples

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	===Simple===		===Simple===
			After the steady state has been reached and the current has reached its maximum value, you attempt to open the circuit. In the short period of time when you open the circuit, what would you expect to happen?

			<math>Solution \:</math> When you open up the circuit, the current <math>I</math> drops from its maximum value to zero. We've observed that the emf across the inductor depends on <math>\frac{dB}{dt}</math> which is ultimately affected by and proportional to <math>\frac{dI}{dt}</math>. In the short period of time when you break the circuit, the change in the current is very large, and thus very large <math>\frac{dI}{dt}</math> is resulted and leads to very large emf across the inductor due to the large <math>\frac{dB}{dt}</math>. Therefore, when you open the circuit, you would observe sparks on the switch.


			===Middling===
	How much time is required for the RL circuit composed of one 1.5<math>V</math> battery, a resistor resistance of 0.5<math>\Omega</math> and an inductor with inductance of 0.03<math>H</math> to reach 60% of the maximum current?		How much time is required for the RL circuit composed of one 1.5<math>V</math> battery, a resistor resistance of 0.5<math>\Omega</math> and an inductor with inductance of 0.03<math>H</math> to reach 60% of the maximum current?

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	<math>\therefore t = 0.0550\: second</math>		<math>\therefore t = 0.0550\: second</math>

	~~<math>~~
	~~\begin{align*}~~
	\\
	~~&= \frac{1.5V}{0.5\Omega} \\~~
	~~&= 3A~~
	~~\end{align*}~~
	~~</math>~~

	<math></math>		<math></math>
	<math></math>		<math></math>

	~~===Middling===~~
	===Difficult===		===Difficult===

Jiwym: /* A Computational Model */

2015-12-06T01:22:24Z

A Computational Model

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	[[File:Rlgraph.png\|2000px\|thumb\|right\|Figure 4. RL circuit current graph<sup>6]]		[[File:Rlgraph.png\|2000px\|thumb\|right\|Figure 4. RL circuit current graph<sup>6]]

	From the above section we were able to see that the current in the RL circuit grows exponentially over time. Figure 4 shows the exponential growth of the current in the RL circuit. For large t, we see that the exponential component becomes zero and thus we obtain <math>I = \frac{emf}{R}</math>. This is when the RL circuit reaches steady state and the current does not change due to steady magnetic flux in the inductor. In RL circuit, there is a value of t for which the exponent of the exponential component becomes a whole number. In other words, <math>t = \frac{L}{R}, \frac{2L}{R}, \frac{3L}{R}, \ldots</math>. This time step is called "time constant" denoted by the Greek letter <math>\tau</math>.		From the above section we were able to see that the current in the RL circuit grows exponentially over time. Figure 4 shows the exponential growth of the current in the RL circuit. For large t, we see that the exponential component becomes zero and thus we obtain <math>I = \frac{emf}{R}</math>. This is when the RL circuit reaches steady state and the current does not change due to steady magnetic flux in the inductor. In RL circuit, there is a value of t for which the exponent of the exponential component becomes a whole number. In other words, <math>t = \frac{L}{R}, \frac{2L}{R}, \frac{3L}{R}, \ldots, \frac{nL}{R}</math>. This time step is called "time constant" denoted by the Greek letter <math>\tau</math>.

	For <math>t = \tau</math>,		For <math>t = \tau</math>,

Jiwym: /* Examples */

2015-12-06T01:21:26Z

Examples

← Older revision		Revision as of 21:21, 5 December 2015
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	<math>(\frac{0.5\Omega}{0.03H})t = 0.916</math>		<math>(\frac{0.5\Omega}{0.03H})t = 0.916</math>

	<math>\therefore t = 0.0550\, second</math>		<math>\therefore t = 0.0550\: second</math>

	<math>		<math>

Jiwym: /* Examples */

2015-12-06T01:04:04Z

Examples

← Older revision		Revision as of 21:04, 5 December 2015
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	<math>(\frac{0.5\Omega}{0.03H})t = 0.916</math>		<math>(\frac{0.5\Omega}{0.03H})t = 0.916</math>

	<math>\therefore t = 0.0550\~~nonumber~~ second</math>		<math>\therefore t = 0.0550\, second</math>

	<math>		<math>

Jiwym: /* Examples */

2015-12-06T01:02:07Z

Examples

← Older revision		Revision as of 21:02, 5 December 2015
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	<math>(\frac{0.5\Omega}{0.03H})t = 0.916</math>		<math>(\frac{0.5\Omega}{0.03H})t = 0.916</math>

	<math>\therefore t = 0.0550 second</math>		<math>\therefore t = 0.0550\nonumber second</math>

	<math>		<math>