Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July...
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Transcript of Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July...
![Page 1: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/1.jpg)
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Lecture 9: Inductance & CapacitanceNilsson 6.1-6.5
ENG17 (Sec. 1): Circuits I
Summer 1 2014
July 8, 2014
![Page 2: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/2.jpg)
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Overview
• Inductors• Capacitors• Series-Parallel L/C• Mutual Inductance• Self Inductance• Energy Stored
![Page 3: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/3.jpg)
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Inductance in the Real World
![Page 4: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/4.jpg)
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What Does an Inductor Look Like?
![Page 5: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/5.jpg)
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What Does an Inductor Do?
• Inductor: electrical component that opposes any change in electrical current
• Associates electrical current and magnetic fields
• Magnetic field generated by charge in motion (i.e., current)
• If current changes wrt time, mag field changes wrt time– Varying mag field results in voltage in linked
conductor
![Page 6: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/6.jpg)
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Add’l Note
• Inductors can store energy through the mag fields– Used in spark plugs
• Inductors do not generate energy, so they are still passive devices
![Page 7: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/7.jpg)
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Inductors in Circuits
Symbol: LUnits: [H] for henrys = [Wb/A]
𝑣=𝐿𝑑𝑖𝑑𝑡
![Page 8: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/8.jpg)
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Determining Voltage
![Page 9: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/9.jpg)
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Current in Inductor
𝑖 (𝑡 )= 1𝐿∫𝑡0
𝑡
𝑣 𝑑𝜏+𝑖(𝑡 0)
![Page 10: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/10.jpg)
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Power & Energy in Inductor
𝑝=𝐿𝑖𝑑𝑖𝑑𝑡
𝑤=12𝐿𝑖2
![Page 11: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/11.jpg)
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Overview
• Inductors• Capacitors• Series-Parallel L/C• Mutual Inductance• Self Inductance• Energy Stored
![Page 12: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/12.jpg)
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Capacitance in the Real World
![Page 13: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/13.jpg)
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What Does a Capacitor Look Like?
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What Does a Capacitor Do?
• Capacitor: electrical component that consists of 2 conductors separated by dielectric
• “Stores” electric charge (like a battery)• Associated with electric fields, due to
separation of charge (voltage)• If voltage varies with time, E-field varies with
time– Varying E-field generates displacement current in
space occupied by field– Capacitance relates displacement current to voltage
![Page 15: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/15.jpg)
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Capacitors in Circuits
Symbol: CUnits: [F] for farads = [C/V]
𝑖=𝐶𝑑𝑣𝑑𝑡
![Page 16: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/16.jpg)
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Capacitor Voltage, Power, & Energy
𝑣 (𝑡 )= 1𝐶∫
𝑡 0
𝑡
𝑖𝑑𝜏+𝑣(𝑡0)
𝑝=𝑣𝑖=𝐶𝑣𝑑𝑣𝑑𝑡
𝑤=12𝐶𝑣2
![Page 17: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/17.jpg)
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Example
𝑣 (𝑡 )={ 0 ,𝑡≤0 𝑠4 𝑡 ,0𝑠≤ 𝑡≤1𝑠4𝑒−(𝑡− 1) ,𝑡≥1𝑠
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ExampleObtain the energy stored in each capacitor under DC conditions.
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Example
Under DC conditions, find i, vc, and iL.Also, find the energy stored in the capacitor and inductor.
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Overview
• Inductors• Capacitors• Series-Parallel L/C• Mutual Inductance• Self Inductance• Energy Stored
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Inductors Series-Parallel
Series Parallel
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Capacitors Series-Parallel
Series Parallel
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Example
![Page 24: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/24.jpg)
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Overview
• Inductors• Capacitors• Series-Parallel L/C• Mutual Inductance• Self Inductance• Energy Stored
![Page 25: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/25.jpg)
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Magnetically Coupled Coils
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Self- and Mutual-Inductance
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Dot Convention
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Mesh Current
![Page 29: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/29.jpg)
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Overview
• Inductors• Capacitors• Series-Parallel L/C• Mutual Inductance• Self Inductance• Energy Stored
![Page 30: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/30.jpg)
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Self Inductance
![Page 31: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/31.jpg)
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Mutual Inductance i.t.o. Self Inductance
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Overview
• Inductors• Capacitors• Series-Parallel L/C• Mutual Inductance• Self Inductance• Energy Stored
![Page 33: Lecture 9: Inductance & Capacitance Nilsson 6.1-6.5 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 July 8, 2014.](https://reader031.fdocuments.in/reader031/viewer/2022012922/5697bffa1a28abf838cc03b3/html5/thumbnails/33.jpg)
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Energy Stored in Magnetically-Coupled Coils
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Recap
• Inductors• Capacitors• Series-Parallel L/C• Mutual Inductance• Self Inductance• Energy Stored