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electrical_engineering_and_electronics_1:block03 [2025/09/28 18:31] – mexleadminelectrical_engineering_and_electronics_1:block03 [2026/01/10 13:27] (aktuell) – mexleadmin
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-====== Block 03 — Electric resistance and power ======+====== Block 03 — Electric Resistance and Power ======
  
-===== Learning objectives =====+===== 3.0 Intro ===== 
 + 
 +==== 3.0.1 Learning Objectives ====
 <callout> <callout>
 +After this 90-minute block, you can
   * Explain and use the passive/active sign convention for power.   * Explain and use the passive/active sign convention for power.
   * Compute electrical **power** $P$ and **energy** $W$ from $U$, $I$, and $t$; show unit consistency.   * Compute electrical **power** $P$ and **energy** $W$ from $U$, $I$, and $t$; show unit consistency.
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 </callout> </callout>
  
-===== 90-minute plan =====+==== 3.0.2 Preparation at Home ==== 
 + 
 +Well, again  
 +  * read through the present chapter and write down anything you did not understand. 
 +  * Also here, there are some clips for more clarification under 'Embedded resources' (check the text above/below, sometimes only part of the clip is interesting).  
 + 
 +For checking your understanding please do the following exercises: 
 +  * 1.6.4 
 +  * 1.6.6 
 +  * 1.7.2 
 + 
 +==== 3.0.3 90-minute plan ====
   - Warm-up (8 min):    - Warm-up (8 min): 
     - recall charge, current, voltage     - recall charge, current, voltage
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   - Wrap-up (5 min): Summary box; common pitfalls checklist.   - Wrap-up (5 min): Summary box; common pitfalls checklist.
  
-===== Conceptual overview =====+==== 3.0.4 Conceptual Overview ====
 <callout icon="fa fa-lightbulb-o" color="blue"> <callout icon="fa fa-lightbulb-o" color="blue">
   - **Power** is the rate of energy conversion: $P=\dfrac{\rm dW}{\rm dt}$. In DC, $W=U\cdot I\cdot t$ and $P=U\cdot I$.   - **Power** is the rate of energy conversion: $P=\dfrac{\rm dW}{\rm dt}$. In DC, $W=U\cdot I\cdot t$ and $P=U\cdot I$.
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 </callout> </callout>
  
-===== Core content =====+===== 3.1 Core Content =====
  
 <WRAP right> <WRAP right>
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 These elements will be considered in more detail below. These elements will be considered in more detail below.
  
-==== Consumer ====+==== 3.1.1 Consumer ====
  
 <WRAP right> <WRAP right>
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Ohmic resistance ====+==== 3.1.2 Ohmic resistance ====
  
 <WRAP right> <WRAP right>
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Linearity of Resistors ====+==== 3.1.3 Linearity of Resistors ====
 <WRAP group><WRAP half column> <WRAP group><WRAP half column>
 <callout color="grey"> <callout color="grey">
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Ideal sources ====+==== 3.1.4 Ideal Sources ====
   * Sources act as generators of electrical energy   * Sources act as generators of electrical energy
   * A distinction is made between ideal and real sources. \\ The real sources are described in the following chapter "[[Block06]]".   * A distinction is made between ideal and real sources. \\ The real sources are described in the following chapter "[[Block06]]".
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   * The specific conductance $\kappa$ is the reciprocal of the specific resistance $\rho$: \\ $\kappa={{1}\over{\rho}}$   * The specific conductance $\kappa$ is the reciprocal of the specific resistance $\rho$: \\ $\kappa={{1}\over{\rho}}$
  
-==== Conductivity of Matter ====+==== 3.1.5 Conductivity of Matter ====
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 <callout color="grey">  <callout color="grey"> 
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-==== Temperature dependence of resistance ====+==== 3.1.6 Temperature Dependence of Resistance ====
  
 The resistance value is - apart from the influences of geometry and material mentioned so far - also influenced by other effects. These are e.g.: The resistance value is - apart from the influences of geometry and material mentioned so far - also influenced by other effects. These are e.g.:
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-==== Power and energy ====+==== 3.1.7 Power and Energy ====
  
 We know that a movement of a charge across a potential difference corresponds to a change in energy.  We know that a movement of a charge across a potential difference corresponds to a change in energy. 
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 </callout> </callout>
  
-==== Efficiency ==== +==== 3.1.8 Passive vs. Active Sign Convention ====
- +
-The usable (= outgoing) $P_{\rm O}$ power of a real system is always smaller than the supplied (incoming) power $P_{\rm I}$.  +
-This is due to the fact, that there are additional losses in reality. \\ +
-The difference is called power loss $P_{\rm loss}$. It is thus valid: +
- +
-$P_{\rm I} = P_{\rm O} + P_{\rm loss}$ +
- +
-Instead of the power loss $P_{\rm loss}$, the efficiency $\eta$ is often given: +
- +
-$\boxed{\eta = {{P_{\rm O}}\over{P_{\rm I}}}\overset{!}{<} 1}$ +
- +
-For systems connected in series (cf. <imgref BildNr23>), the total resistance is given by: +
- +
-$\boxed{\eta = {{P_{\rm O}}\over{P_{\rm I}}} = {\not{P_{1}}\over{P_{\rm I}}}\cdot {\not{P_{2}}\over \not{P_{1}}}\cdot {{P_{\rm O}}\over \not{P_{2}}} = \eta_1 \cdot \eta_2 \cdot \eta_3}$ +
- +
-<WRAP> +
-<imgcaption BildNr23 | Power flow diagram> +
-</imgcaption> +
-{{drawio>Leistungsfluss.svg}} +
- +
-</WRAP> +
- +
-~~PAGEBREAK~~ ~~CLEARFIX~~ +
-==== Passive vs. active sign convention ====+
    
 For **loads** (passive convention): current enters the $+$ terminal; $P=U\cdot I>0$ → absorption.   For **loads** (passive convention): current enters the $+$ terminal; $P=U\cdot I>0$ → absorption.  
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-===== Common pitfalls =====+===== 3.2 Common Pitfalls =====
   * Don’t mix conventions: use **passive** for loads when computing $P=U\cdot I$ as absorbed power.   * Don’t mix conventions: use **passive** for loads when computing $P=U\cdot I$ as absorbed power.
   * Always attach **units** (e.g., $I=2~{\rm A}$). Check $P$ with **two forms** ($R I^2$ vs. $U^2/R$) to catch arithmetic slips.   * Always attach **units** (e.g., $I=2~{\rm A}$). Check $P$ with **two forms** ($R I^2$ vs. $U^2/R$) to catch arithmetic slips.
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   * Temperature law is **approximate** near the reference (often $20^\circ\rm C$); large $\Delta T$ or semiconductors need better models.   * Temperature law is **approximate** near the reference (often $20^\circ\rm C$); large $\Delta T$ or semiconductors need better models.
  
-===== Exercises =====+===== 3.3 Exercises =====
 ==== Worked examples ==== ==== Worked examples ====
  
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 Which wire cross-section $A_{\rm Cu}$ must be selected? Which wire cross-section $A_{\rm Cu}$ must be selected?
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 #@HiddenEnd_HTML~pow2,Result ~@# #@HiddenEnd_HTML~pow2,Result ~@#
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