R=20 Ω
V=10 V
The switch in the circuit is closed at t=0.
L=10 H
" = !L
di
dt
What is the initial current in the
inductor, immediately after the
switch is closed (at t=0+) ?
A) 0 A
B) 0.5 A
C)1.0 A
D) 2 A
E) None of these.
1
R=20 Ω
V=10 V
The switch in the circuit is closed at t=0.
L=10 H
" = !L
di
dt
What is the initial current in the
inductor, immediately after the
switch is closed (at t=0+) ?
A) 0 A
B) 0.5 A
C)1.0 A
D) 2 A
E) None of these.
2
CAPA #13 is due Friday
New online participation survey is still up!
Reading: 34.3-5
_________________________
Last: Inductors in circuits
Today: Inductors, and AC circuits
Next: Maxwell's equations, putting it all together!
3
1
Clicker Question The switch in the circuit below is closed at t=0.
What is the initial rate of change of
current di/dt in the inductor,
immediately after the switch is
closed ?
R=20 Ω
V=10 V
L=10 H
A) 0 A/s
B) 0.5A/s
C)1A/s
D) 10A/s
E) None of these.
Hints: What is the initial current through the circuit?
Given that - what is the initial voltage across the inductor?
4
Clicker Question The switch in the circuit below is closed at t=0.
V = 10V
Before t=0,
V=?
V=?
R=20 Ω
L = 10H
What is the initial rate of change of
current di/dt in the inductor,
immediately after the switch is
closed ?
A) 0 A/s
B) 0.5A/s
C)1A/s
D) 10A/s
E) None of these.
Hints: What is the initial current through the circuit?
Given that - what is the initial voltage across the inductor?
V=0
" = !L
di
dt
5
Clicker Question The switch in the circuit below is closed at t=0.
R=20 Ω Before t=0,
V=?
V=0
V = 10V
L = 10H
What is the initial rate of change of
current di/dt in the inductor,
immediately after the switch is
closed ?
A) 0 A/s
B) 0.5A/s
C)1A/s
D) 10A/s
E) None of these.
Hints: What is the initial current through the circuit?
Given that - what is the initial voltage across the inductor?
V=0
6
2
Clicker Question The switch in the circuit below is closed at t=0.
V=10
V = 10V
V=10!
V=0
R=20 Ω
L = 10H
What is the initial rate of change of
current di/dt in the inductor,
immediately after the switch is
closed ?
A) 0 A/s
B) 0.5A/s
C)1A/s
D) 10A/s
E) None of these.
Hints: What is the initial current through the circuit?
Given that - what is the initial voltage across the inductor?
V=0
7
Clicker Question The switch in the circuit below is closed at t=0.
V=10
V = 10V
R=20 Ω
At t=0+,
V=?
L = 10
What is the initial rate of change of
current di/dt in the inductor,
immediately after the switch is
closed ?
A) 0 A/s
B) 0.5A/s
C)1A/s
D) 10A/s
E) None of these.
Hints: What is the initial current through the circuit?
Given that - what is the initial voltage across the inductor?
V=0
di
" = !L
dt
8
Clicker Question The switch in the circuit below is closed at t=0.
V=10 R = 20!
V = 10V
V=10!!
(briefly)
L = 10H
What is the initial rate of change of
current di/dt in the inductor,
immediately after the switch is
closed ?
A) 0 A/s
B) 0.5A/s
C)1A/s
D) 10A/s
E) None of these.
Hints: What is the initial current through the circuit?
Given that - what is the initial voltage across the inductor?
V=0
9
3
Clicker Question The switch in the circuit below is closed at t=0.
V=10 R = 20!
V = 10V
V=10!!
(briefly)
L = 10H
What is the initial rate of change of
current di/dt in the inductor,
immediately after the switch is
closed ?
A) 0 A/s
B) 0.5A/s
C)1A/s
D) 10A/s
E) None of these.
Hints: What is the initial current through the circuit?
Given that - what is the initial voltage across the inductor?
V=0
" = !L
di
dt
Answer: I(initial)=0, so it must still be 0. Thus, ΔV(across R)=0
V(across inductor) = V(batt!) , but also V(inductor) = L di/dt.
So at t=0+, di/dt = V(batt)/L = 10V/10H = 1 A/s.
10
Clicker Question
An LR circuit is shown below. Initially the switch is open. At
time t=0, the switch is closed. What is the current thru the
inductor L immediately after the switch is closed (time = 0+)?
R1 = 10Ω
V = 10V
L = 10H
R2 = 10Ω
A) Zero
B) 1 A
C) 0.5A
D) None of these.
11
Clicker Question
An LR circuit is shown below. Initially the switch is open. At
time t=0, the switch is closed.
R1 = 10Ω
V = 10V
L = 10H
R2 = 10Ω
After a long time, what is the current from the battery?
A) 0A
B) 0.5A
C) 1.0A
D) 2.0A
E) None of these.
12
4
AC Circuits
The Voltage in your wall sockets at home is AC.
AC stands for Alternating Current, but would perhaps more
appropriately be called Alternating Voltage.
Alternating = Sinusoidal with time
13
V (t ) = V peak sin(!t )
" = 2!f =
2!
T
ω is the radial frequency (radians / second)
f is the frequency in (cycles / second = Hertz)
T is the period in (seconds), i.e. time for one cycle
14
In the United States of America
f = 60 cycles/second or Hertz
T = (1 / 60) seconds
Vpeak = 170 Volts
One might be interested in something like the average Voltage.
But, the average V(t) = 0.
15
5
Vrms = V (root mean square) =
V2
Time Average of Voltage squared.
Vrms = V p
sin 2 (!t ) = V p 1 / 2 = V p / 2
Time Average of sin2 or cos2 over many cycles = 1/2
Vrms = 170V / 2 = 120 Volts
This is how we refer to the
US Standard Voltage.
16
The term “AC Voltage” or “VAC” means
Vrms = V peak / 2
The term “AC Current” [somewhat redundant] means
irms = i peak / 2
RMS values of AC Voltage and Current are always implied if
not explicitly stated otherwise. This is because the old DC
formulas involving V, i, R, P (power) all hold for AC circuits if
we use the RMS values.
17
Example: AC Voltage across a resistor
V (t ) = V p sin(!t )
VAC
~
R
i (t ) =
V V p sin(!t )
=
= i peak sin(!t )
R
R
P(t ) = iV = i peakV p sin 2 (!t )
Instantaneous Power is oscillating from zero to maximum.
18
6
We might be interested in the average (over time) power
delivered to the resistor.
P(t ) = iV = i peakV peak sin 2 (!t )
1
< P(t ) >= i peakV peak < sin 2 (!t ) >= i peakV peak
2
& 1
#& 1
#
< P(t ) >= $
i peak !$
V peak !
% 2
"% 2
"
Pave = irmsVrms
Same form as before, but now RMS values.
19
CT 33.35
A 100 W light bulb is attached to a wall plug. (120 VAC, 60 Hz)
What is the peak power output to the bulb?
A) 100 W
B) Sqrt[2]*100 W = 141 W
C) 200 W
D) Other
21
CT 33.36
A 600 Watt hairdryer is attached to 120 VAC
circuit. What is the peak current through the
hairdryer (to within 5%)?
A: 0 A B) 5 A
E) Other
C) 7 A
D) 10 A
P = IV, which means P(ave) = I(rms)* V(rms)
600 W = I(rms) * 120 V
=> I(rms) = 600/120 = 5 A.
But I(peak) = I(rms)*Sqrt[2] = 5*1.4, about 7.
22
7
CT 33.37
The instantaneous power consumed by my De-luxe Toaster
Oven looks like this as a function of time:
23
CT 33.38
1200 W
Which of the following is correct?
P ave
V rms
I rms
A: 1200 W 120 V 10 A (=1200/120)
B: 1200 W 170 V
7 A (=1200/170)
C: 600 W
120 V
5 A (= 600/120)
D: 600 W
170 V
3.5 A (=600/170)
E: None of the above is right.
24
CT 33.39
What is "T" in the picture (in the USA)?
A: 1/30 s
B: 1/60 s
C: 1/120 s
D: Other
25
8