Self-Inductance. Φ i. Self-induction. = (if flux Φ 1 through 1 loop. Tm Vs A A. Lecture 11-1

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1 Lecture - Self-Inductance As current i through coil increases, magnetic flux through itself increases. This in turn induces back emf in the coil itself When current i is decreasing, emf is induced again in the coil itself in such a way as to slow the decrease. L Φ i L self-inductance Self-induction NΦ i (if flux Φ through loop unit: henry is linked by N loops) H Tm Vs A A Faraday s Law Δi ε L

2 Lecture - Behavior of Inductors Increasing Current Initially, the inductor behaves like a battery connected in reverse. After a long time, the inductor behaves like a conducting wire. Decreasing Current Initially, the inductor behaves like a reinforcement battery. After a long time, the inductor behaves like a conducting wire.

3 Lecture -3 Physics 9 Question February 5,. The switch in this circuit has been open for a long time. Then the switch is closed at t. What is the magnitude of the current through the resistor immediately after the switch is closed? a) zero b) V/L c) R / L d) V / R e) V/R

4 Lecture -4 Example The switch was closed and remains closed for a long time. What is the current through R? a) V /(R +R ) b) V/R c) V/R d) V/L e) zero

5 Lecture -5 Mutual Inductance Total magnetic flux through coil due to the field created by coil : Φ Then, Φ I Define mutual inductance of coil with respect to coil ε ΔΦ M ΔI Reverse the roles of coil and coil ε ΔΦ M ΔI M similarly M Φ I Φ I unit: henry Reciprocity a fundamental symmetry M M Tm A M Vs A

Lecture -6 Solenoid: Archetypical Inductor Current i flows through a long solenoid of radius r with N turns in length l r << l For each turn For the solenoid or B L N μ i

6 Lecture -6 Solenoid: Archetypical Inductor Current i flows through a long solenoid of radius r with N turns in length l r << l For each turn For the solenoid or B L N μ i l A π r Φ N BA μ iπr l L μ B r l r N Φ B N N μ π μ π i l l n Al ε μ nal Δi [ ] μ H m / Inductance, like capacitance, only depends on geometry (if made of conductor and air)

7 Lecture -7 Energy Stored By Inductor. Switch on at t. Loop Rule: 3. Multiply through by I Δ I ε IR L Rate at which battery is supplying energy ΔI ε I I R+ LI Rate at which energy is dissipated by the resistor Rate at which energy is being stored in inductor L Compare with capacitor: Q Q Δ VI, U Q E C C UB LI

8 Lecture -8 Where is the Magnetic Energy Stored? Energy must be stored in the magnetic field! Energy stored by a capacitor is stored in its electric field Consider a long solenoid where B μ N Φ B ni, L I μ B area A ( ) UB LI μn Al I Al μ n Al Soenergy density of the magnetic field is ue u B U Al B B μ εe (Energy density of the electric field) length l

Lecture -9 Alternating Current (AC) Electric current that

wire that rotates in a uniform magnetic field.

9 Lecture -9 Alternating Current (AC) Electric current that changes direction periodically ac generator is a device which creates an ac emf/current. A sinusoidally oscillating EMF is induced in a loop of wire that rotates in a uniform magnetic field. Φ B NBAcosθ NBAcosωt ΔΦ ε B ( NBA ω)sinω t where ω π f π T ac motor ac generator run in reverse

10 Lecture - Electric meter Hot Neutral Electricity in the Home Hot Household outlets usually supply v rms -V at f 6Hz. Power line transformer has 3 taps. Kilowatt hour 76V hot Vrms Vrms hot neutral Two hot wires > 4V Third prong is local ground. Dryer Lamp TV Computer Microwave

11 Lecture - Resistive Load Start by considering simple circuits with one element (R, C, or L) in addition to the driving emf. Pick a resistor R first. Kirchhoff s Loop Rule: () () ( ) ε t i t R, ε t ε sinωt + a () () V t i t R ε sinωt R V ε V V i() t sinω R v R (t) and i(t) in phase I

12 Lecture - Power Dissipated by Resistive Load V(t) ε (t) T Power: ( ) P i R I sinωt R ( ) I R sin ωt sin T ωt sin ωtdt T

13 Lecture -3 3 Average power: P i R I Rsin ωt av but sin ω t sin ω t Pav I P I R I av rms rms R, thus I I

14 Lecture -4 4 Mean vs Root-Mean-Square it () I sinωt Irms i I.77 I i I sin ωt I P I I ε I av R rmsr rms rms

15 Lecture -5 5 Physics 9 Question February 5,. The ac voltage from a wall outlet is V rms. What is the voltage? a) 6V b) V c) 7V d) 4V e) zero

C C, ωc v L (t) leads I(t) by 9 + -- X I P C

16 Lecture -6 6 Capacitive vs Inductive Load I(t) leads v(t) by 9 capacitive reactance V X C C, ωc v L (t) leads I(t) by X I P C av v L inductive reactance X L ωl + -- V L, X L I

Chapter 33. Alternating Current Circuits

Chapter 33. Alternating Current Circuits Chapter 33 Alternating Current Circuits 1 Capacitor Resistor + Q = C V = I R R I + + Inductance d I Vab = L dt AC power source The AC power source provides an alternative voltage, Notation - Lower case