Lecture B
Voltage dividers
Impedance
Complex numbers
Lecture B
Voltage dividers
Impedance
Complex numbers
B1a
5W
I3
What is I3?
A) 2 A
B) 4 A
C) 5 A
D) 10 A
E) 14.5 A
4W
1W
+
10 V
B1b
5W
I3 = 2 A
What is IBatt?
A) 2 A
B) 4 A
C) 5 A
D) 10 A
E) 14.5 A
4W
1W
+
10 V
IBatt = ?
B2
What is Vout/Vin?
R1
A)
R1  R2
R2
D)
R1
R2
B)
R1  R2
E)
C) R1  R2
R2
R1
R2
Things you need to know about complex
numbers for Phys3330
1.Perform algebraic operations on complex numbers and
represent a given complex number graphically and express it
in polar form.
2. Represent a sinusoidal function as the real and imaginary
part of an exponential and use this representation for adding
trigonometric functions.
3. Set up a linear differential equation to describe the behavior
of LCR circuit that is subject to an applied sinusoidal voltage.
4. Use complex exponentials to solve homogenous and
inhomogeneous linear differential equations with constant
coefficients.
1. Complex number - The imaginary unit:
General complex number
real part of z, x= Re z
and
, where x & y are REAL numbers
imaginary part of z, y= Im z
Arithmetic with complex numbers z1,2:
+
−
×
÷
1
Complex conjugate (z → z*) : Replace i with -i
→
→ the modulus of z
2. Power Series for exponential and trigonometric functions:
Euler’s Formula
Now compare trigonometric and hyperbolic function in complex number:
3. Polar representation of a complex number z=x+iy
y (imaginary)
Representing z=x+iy by the point (x,y)
z=x+iy
Then,
r
ϕ
x (real)
where,
So we can always write
x
y
✵Polar representation is advantageous for multiplication and division!
Let
then
B3
L
R
What is Zeq?
1
1
A) 
R j L
D) R 
1
1 
B)  

R
j

L


1
j L
1
C) R  j L

1 
E)  R 

j

L


1
Aliasing
Red = real signal
Blue = scope display
Black points = sampling times
B4
Is it possible to measure the current generated
by the power supply using the scope?
A) No, it only measures voltage
B) Yes, just turn the knob on the scope from
“V” to “I”
C) Yes, put a resistor in the circuit and measure
the voltage across it.
B5
To measure the current thru resistor 3, how should
the ammeter be attached?
a)
d)
1
A
3
A
A
4
A
b)
12 V
2
c)
e) MORE than one of these choices is ok.
B6
An ideal ammeter should have
A) Zero resistance
B) Infinite resistance
C) A well defined resistance >
A) 0W (e.g. 1W or 1kW)
D) Shiny red color
B7
To measure the voltage across resistor 3, how should the
voltmeter be attached (assume you only attach one at a time)?
a)
d)
1
V
3
V
V
4
V
b)
12 V
2
c)
e) MORE than one of these choices is ok.
B8
An ideal voltmeter should have
A)
B)
C)
D)
Zero resistance
Infinite resistance
A well defined resistance >0W (e.g. 1W or 1kW)
Shiny red color