5-energy Storage Elements
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ELECTRIC CIRCUITS THEORY 1 These lecture slides have been compiled by Mohammed LECTURE 5 SalahUdDin Ayubi. Energy Storage Elements 20 August 2005
Engineer M S Ayubi
1
Outline • Capacitors • Inductors • Frequency Effects – Static (unchanging with time) analysis – Dynamic (changing with time) analysis
20 August 2005
Engineer M S Ayubi
2
Outline • Capacitors • Inductors • Frequency Effects – Static (unchanging with time) analysis – Dynamic (changing with time) analysis
20 August 2005
Engineer M S Ayubi
3
Capacitors
• Q = CV charge = capacitance * voltage • Unit: Farad (F) F = C/V • Typical values are pF to uF 20 August 2005
Engineer M S Ayubi
4
Capacitors
20 August 2005
Engineer M S Ayubi
5
Capacitors Power
Energy
20 August 2005
Engineer M S Ayubi
6
Capacitors • Parallel • Series
20 August 2005
Engineer M S Ayubi
7
Outline • Capacitors • Inductors • Frequency Effects – Static (unchanging with time) analysis – Dynamic (changing with time) analysis
20 August 2005
Engineer M S Ayubi
8
Inductors • Coil made up of n turns of wire
20 August 2005
Engineer M S Ayubi
9
Inductors ∀ φ =magnetic flux (unit: Wb) ∀ φ =Li =inductance * current dφ V =N dt
Nφ
Faraday’s Law Magnetic field
20 August 2005
Engineer M S Ayubi
10
Inductors • L = inductance • Unit: Henry (H)
20 August 2005
Engineer M S Ayubi
11
Inductors
20 August 2005
Engineer M S Ayubi
12
Inductors
20 August 2005
Engineer M S Ayubi
13
Inductors Parallel Leq = L1 || L2 || L3 …
Series Leq = L1 + L2 + L3 …
20 August 2005
Engineer M S Ayubi
14
Outline • Capacitors • Inductors • Frequency Effects – Static (unchanging with time) analysis – Dynamic (changing with time) analysis
20 August 2005
Engineer M S Ayubi
15
Frequency Effects • Low frequency (f ⇒ 0, t ⇒ ∞) – Capacitor • I=C dv/dt, so I=0 (open)
– Inductor • V = L di/dt, so V=0 (short)
• High frequency (f ⇒ ∞, t ⇒ 0) – Capacitor • I=C dv/dt, but I ≠ ∞, so V cannot change instantly
– Inductor • V = L di/dt, but V ≠ ∞, so I cannot change instantly
20 August 2005
Engineer M S Ayubi
16
Low Frequency (Constant)
20 August 2005
Engineer M S Ayubi
17
Find Vx
20 August 2005
Engineer M S Ayubi
18
High Frequency (Instant)
20 August 2005
Engineer M S Ayubi
19
Dynamic Circuit Analysis Two Approaches to solving circuits with energy storage elements and time-varying inputs: • Transient Analysis (time-domain) • Phasor Analysis (frequency-domain)
20 August 2005
Engineer M S Ayubi
20
Find Vx
20 August 2005
Engineer M S Ayubi
21
Engineer M S Ayubi
1
Outline • Capacitors • Inductors • Frequency Effects – Static (unchanging with time) analysis – Dynamic (changing with time) analysis
20 August 2005
Engineer M S Ayubi
2
Outline • Capacitors • Inductors • Frequency Effects – Static (unchanging with time) analysis – Dynamic (changing with time) analysis
20 August 2005
Engineer M S Ayubi
3
Capacitors
• Q = CV charge = capacitance * voltage • Unit: Farad (F) F = C/V • Typical values are pF to uF 20 August 2005
Engineer M S Ayubi
4
Capacitors
20 August 2005
Engineer M S Ayubi
5
Capacitors Power
Energy
20 August 2005
Engineer M S Ayubi
6
Capacitors • Parallel • Series
20 August 2005
Engineer M S Ayubi
7
Outline • Capacitors • Inductors • Frequency Effects – Static (unchanging with time) analysis – Dynamic (changing with time) analysis
20 August 2005
Engineer M S Ayubi
8
Inductors • Coil made up of n turns of wire
20 August 2005
Engineer M S Ayubi
9
Inductors ∀ φ =magnetic flux (unit: Wb) ∀ φ =Li =inductance * current dφ V =N dt
Nφ
Faraday’s Law Magnetic field
20 August 2005
Engineer M S Ayubi
10
Inductors • L = inductance • Unit: Henry (H)
20 August 2005
Engineer M S Ayubi
11
Inductors
20 August 2005
Engineer M S Ayubi
12
Inductors
20 August 2005
Engineer M S Ayubi
13
Inductors Parallel Leq = L1 || L2 || L3 …
Series Leq = L1 + L2 + L3 …
20 August 2005
Engineer M S Ayubi
14
Outline • Capacitors • Inductors • Frequency Effects – Static (unchanging with time) analysis – Dynamic (changing with time) analysis
20 August 2005
Engineer M S Ayubi
15
Frequency Effects • Low frequency (f ⇒ 0, t ⇒ ∞) – Capacitor • I=C dv/dt, so I=0 (open)
– Inductor • V = L di/dt, so V=0 (short)
• High frequency (f ⇒ ∞, t ⇒ 0) – Capacitor • I=C dv/dt, but I ≠ ∞, so V cannot change instantly
– Inductor • V = L di/dt, but V ≠ ∞, so I cannot change instantly
20 August 2005
Engineer M S Ayubi
16
Low Frequency (Constant)
20 August 2005
Engineer M S Ayubi
17
Find Vx
20 August 2005
Engineer M S Ayubi
18
High Frequency (Instant)
20 August 2005
Engineer M S Ayubi
19
Dynamic Circuit Analysis Two Approaches to solving circuits with energy storage elements and time-varying inputs: • Transient Analysis (time-domain) • Phasor Analysis (frequency-domain)
20 August 2005
Engineer M S Ayubi
20
Find Vx
20 August 2005
Engineer M S Ayubi
21
