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electrical_engineering_1:dc_circuit_transients [2021/11/03 15:21]
tfischer 		electrical_engineering_1:dc_circuit_transients [2022/04/22 21:16]
tfischer
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-====== 5. DC Circuit Transients (ob RC elements) ======+====== 5. DC Circuit Transients (on RC elements) ======
  
 <WRAP onlyprint> <WRAP onlyprint>
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 <callout> <callout>
  
-=== Goals ===+=== Learning Objectives ===
  
-After this lesson, you should: +By the end of this section, you will be able to: 
- +  - know the time constant $\tau$ and in particularly calculate it. 
-  - know the time constant $\tau$ and in particular be able to calculate it. +  - determine the time characteristic of the currents and voltages at the RC element for a given resistance and capacitance.
-  - Be able to determine the time characteristic of the currents and voltages at the RC element for a given resistance and capacitance.+
   - know the continuity conditions of electrical quantities.   - know the continuity conditions of electrical quantities.
   - know when (=according to which measure) the capacitor is considered to be fully charged / discharged, i.e. a steady state can be considered to have been reached.   - know when (=according to which measure) the capacitor is considered to be fully charged / discharged, i.e. a steady state can be considered to have been reached.
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 </callout> </callout>
  
-<WRAP>{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjCAMB0l3BOJyWoVaYEBYDsuBmbSbMSAVmwDZcqRyJyRsD6BTAWjDACgA3cNmwgATMUHCwQqDPFNIMmOR4AnEAQJ0pw4gu0yykHgGNmcCWYViFN2PEgjFd3gHcL10eI9G3Hj7s8bHl8vUL1aKB4AZVEADlj3ci1pGxAAMwBDABsAZzYZEWDRJPARBP0wMsi3CqqKlKKRErAqK3EWoJC9VsDwCKMAD09ccEh0ESpWbkdhMRAoniGWqdjHMFi9WKZZ4QBVRfAN8AQV9Cw6SQScg4JcSSx1BAhKmc8QACUbnpEx9XxRSrMN4AYR4tys8QsGmSkkUPAADsxsOVpEIEh4IJ0kejxAFvEU0RYAvpBqIEFpAQRIM8wNs3gBLG7U0oKAhgKYiViXECgoZ4ST-ZFaI7c3nMchnXAKPBrQhAuYAVx4AHtROBZGN0DB7LQRCccOQ2U0MPYELQksarGrWPSAPrAgA0AB0cgr7WD0U57Mztaa0P6kDyMvCMsZ6QAXDIAO2MbBdoII5QMengHzYOXpOUjMbjOU+QA noborder}} </WRAP> +In the simulation on the below you can see the circuit mentioned above in a slightly modified form:
- +
-In the simulation on the right you can see the circuit mentioned above in a slightly modified form:+
  
   * The capacitance $C$ can be charged via the resistor $R$ if the toggle switch $S$ connects the DC voltage source $U_s$ to the two.   * The capacitance $C$ can be charged via the resistor $R$ if the toggle switch $S$ connects the DC voltage source $U_s$ to the two.
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   - Become familiar with how the capacitor current $i_C$ and capacitor voltage $u_C$ depend on the given capacitance $C$ and resistance $R$. \\ To do this, use for $R=\{ 10\Omega, 100\Omega, 1k\Omega\}$ and $C=\{ 1\mu F, 10 \mu F\}$. How fast does the capacitor voltage $u_C$ increase in each case n?   - Become familiar with how the capacitor current $i_C$ and capacitor voltage $u_C$ depend on the given capacitance $C$ and resistance $R$. \\ To do this, use for $R=\{ 10\Omega, 100\Omega, 1k\Omega\}$ and $C=\{ 1\mu F, 10 \mu F\}$. How fast does the capacitor voltage $u_C$ increase in each case n?
   - Which quantity ($i_C$ or $u_C$) is continuous here? Why must this one be continuous? Why must the other quantity be discontinuous?   - Which quantity ($i_C$ or $u_C$) is continuous here? Why must this one be continuous? Why must the other quantity be discontinuous?
 +
 +<WRAP>{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjCAMB0l3BOJyWoVaYEBYDsuBmbSbMSAVmwDZcqRyJyRsD6BTAWjDACgA3cNmwgATMUHCwQqDPFNIMmOR4AnEAQJ0pw4gu0yykHgGNmcCWYViFN2PEgjFd3gHcL10eI9G3Hj7s8bHl8vUL1aKB4AZVEADlj3ci1pGxAAMwBDABsAZzYZEWDRJPARBP0wMsi3CqqKlKKRErAqK3EWoJC9VsDwCKMAD09ccEh0ESpWbkdhMRAoniGWqdjHMFi9WKZZ4QBVRfAN8AQV9Cw6SQScg4JcSSx1BAhKmc8QACUbnpEx9XxRSrMN4AYR4tys8QsGmSkkUPAADsxsOVpEIEh4IJ0kejxAFvEU0RYAvpBqIEFpAQRIM8wNs3gBLG7U0oKAhgKYiViXECgoZ4ST-ZFaI7c3nMchnXAKPBrQhAuYAVx4AHtROBZGN0DB7LQRCccOQ2U0MPYELQksarGrWPSAPrAgA0AB0cgr7WD0U57Mztaa0P6kDyMvCMsZ6QAXDIAO2MbBdoII5QMengHzYOXpOUjMbjOU+QA noborder}} </WRAP>
  
 At the following, this circuit is divided into two separate circuits, which consider only charging and only discharging. At the following, this circuit is divided into two separate circuits, which consider only charging and only discharging.
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-<WRAP> <imgcaption imageNo02 | circuit for viewing the charge curve> </imgcaption> {{drawio>SchaltungEntladekurve2}} </WRAP>+Here a short introduction about the transient behavior of an RC element (starting at 15:07 until 24:55) 
 +{{youtube>8nyNamrWcyE?start=907&stop=1495}}
  
 To understand the charging process of a capacitor, an initially uncharged capacitor with capacitance $C$ is to be charged by a DC voltage source $U_s$ via a resistor $R$. To understand the charging process of a capacitor, an initially uncharged capacitor with capacitance $C$ is to be charged by a DC voltage source $U_s$ via a resistor $R$.
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   * With the current thus reduced, less charge flows on the capacitor.   * With the current thus reduced, less charge flows on the capacitor.
   * Ideally, the capacitor is not fully charged to the specified voltage $U_s$ until $t \rightarrow \infty$. It then carries the charge: $q(t \rightarrow \infty)=Q = C \cdot U_s$   * Ideally, the capacitor is not fully charged to the specified voltage $U_s$ until $t \rightarrow \infty$. It then carries the charge: $q(t \rightarrow \infty)=Q = C \cdot U_s$
 +
 +<WRAP> <imgcaption imageNo02 | circuit for viewing the charge curve> </imgcaption> {{drawio>SchaltungEntladekurve2}} </WRAP>
  
 The process is now to be summarized in detail in formulas. Linear components are used in the circuit, i.e. the component values for the resistor $R$ and the capacitance $C$ are independent of the current or the voltage. Then definition equations for the resistor $R$ and the capacitance $C$ are also valid for time-varying or infinitesimal quantities: The process is now to be summarized in detail in formulas. Linear components are used in the circuit, i.e. the component values for the resistor $R$ and the capacitance $C$ are independent of the current or the voltage. Then definition equations for the resistor $R$ and the capacitance $C$ are also valid for time-varying or infinitesimal quantities:
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 <callout> <callout>
  
-=== Goals === +=== Learning Objectives ===
- +
-After this lesson, you should:+
  
-  - Be able to calculate the energy content in a capacitor. +By the end of this section, you will be able to: 
-  - Be able to calculate the change in energy of a capacitor resulting from a change in voltage between the capacitor terminals. +  - calculate the energy content in a capacitor. 
-  - Be able to calculate (initial) current, (final) voltage and charge when balancing the charge of several capacitors (also via resistors).+  - calculate the change in energy of a capacitor resulting from a change in voltage between the capacitor terminals. 
 +  - calculate (initial) current, (final) voltage and charge when balancing the charge of several capacitors (also via resistors).
  
 </callout> </callout>