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UNIVERSITY OF OSLO
Faculty of Mathematics and Natural Sciences
Exam in: INF1411
Day of exam: Monday June 3rd 2013
Exam hours: 14.30-18.30
This examination paper consists of 6 pages
Appendices: None
Permitted materials: All printed and written, and pocket calculator
Make sure that your copy of this examination paper is complete before answering.
Problem 1 – Ohms’s law, Kirchhoff’s current and voltage laws (20%)
Problem 1a)
Find the current i through the resistor R in Figur 1.
i
R=1kΩ
v=5sint(t)
Figur 1
Problem 1b)
Find the current through a resistor when it consumes 5W and the voltage drop across it is
10V, and then find the resistance value of R.
Problem 1c)
Find the current i in Figur 2
R=147Ω
5V
C=3μF
i
Figur 2
Problem 1d)
Find the currect ix in Figur 3
Figur 3
Problem 1e)
Consider the circuit in Figur 4. Assume that Vs is a direct voltage source. What is Vx equal to
in this case?
R1=1kΩ
Vs
C1=0,1μF
Vx
R2=3kΩ
R3=3kΩ
Figur 4
If Vs is replaced by an alternating voltage source with a very high frequency, what will Vx
become approximately equal to in this case?
Problem 2 – RC circuits (weight 20%)
R=10kΩ
Batteri
V=25v
+
Vc
-
C=0,001μF
Figur 5
Problem 2a)
Given the circuit in Figur 5: Assume that the switch is being closed at time t0, and that the
capacitor is completely discharged before t0. Draw a graph showing the voltage across the
capacitor as a function of time, and start in t0. Up to what point in time does it make sense to
draw the charging curve?
Problem 2b)
Calculate how long it will take before the voltage drop Vc has reached 15volt by using
calculations (i.e. do not ready the value from the curve drawn in problem 2a).
Problem 2c)
Now assume that the switch is being opened again after Vc has reached its maximum value.
How long will it take before Vc has reached 10 volt? You can choose whether you would like
to find this answer by drawing a graph or making calculations.
Problem 2d)
The battery is now being replaced by a voltage source which produces a sinusoid with a
frequency of 20 kHz and amplitude of 10 volt. Find the impedance by drawing a phase
diagram for the circuit, and calculate the phase angle between the voltage source and the
capacitor.
Problem 2e)
What is the phase angle between the voltage over the capacitor and the resistor?
Problem 3 – Operational amplifiers
Problem 3a)
R1=1kΩ
R2=2kΩ
Vin
R3=5kΩ
Vout
+
Figur 6
Find the gain A of the circuit in Figur 6.
Problem 3b)
Cf
Vin
Rin
Vout
Figur 7
The circuit shown in Figur 7 has three different names, depending on how it is being used.
What are the three uses/functions?
Problem 3c)
What type of circuit will you get if the capacitor and resistor switch place? Assume then that
the output signal Vout is as shown in Figur 8. Draw what the corresponding input signal Vin
must look like.
Figur 8
Problem 3d)
The circuit shown in Figur 9 is called a comparator. Find the values of R1 and R2 if the
circuit is to determine if Vin is smaller or larger than 4,5 volt. The maximum current through
R1 shall not exceed 100mA, and operational amplifier is considered ideal.
+12V
R1
Vout
Vin
+
R2
Figur 9
Problem 4 – Diodes and transistors (weight 20%)
Problem 4a)
Vin
Vout
R
Figur 10
Given the diode circuit in Figur 10. Draw Vout when Vin is a triangular pulse signal as
shown in Figur 11.
Figur 11
Problem 4b)
Given the circuit in Figur 12. Derive an approximate expression for Vb as a function of VCC,
R1 and R2, and then determine VE. Use the following values: VCC=25V, R1=22kΩ,
R2=10kΩ, RC=1kΩ, RE=1kΩ and ß=250
Vcc
R1
Rc
VC
Vin
Vout
VB
VE
R2
Re
Figur 12
Problem 4c)
Why does the expression for calculating VB as a function of R1, R2 and VCC give an
approximation only? If you were to find the exact value, what must then be taken into
consideration as well? (You are not supposed to find this expression, just explain what needs
to be included).
Problem 4d)
Assume now that R1 is being replaced by another resistor Rx. What is the largest value Rx
can have if there is to flow a collector current Ic (i.e. if Rx is larger than this value, there will
be no current Ic)?
Problem 5 – Multiple choice
For each group of statements below, only one statement is correct. Your answer shall consist
of the letter designating what you claim is the correct statement. Please read carefully through
all statements of each group before you give your answer!
Problem 5-1)
In a bipolar transistor
a) there is no current Ib through the base
b) the collector current Ic and emitter current Ie are equal
c) there are no depletion regions
d) the collector current Ic is proportional to the base current Ib when the transistor is in
the linear region
e) the charge carriers are protons
Problem 5-2)
An ideal operational amplifier has
a) infinitely small input resistance
b) infinitely high slew rate
c) infinitely small gain
d) input resistance proportional to the frequency
e) finite amplification
Problem 5-3)
Kirchhoff’s current and voltage laws
a) Kirchhoff’s current and voltage laws replace Ohm’s law
b) Kirchhoff’s voltage law does not apply to alternating voltages
c) Kirchhoff’s current law does only apply to direct currents
d) Kirchhoff’s current law can be explained with the fact that charges cannot be created
or disappear spontaneously in a node
e) None of the statements above are correct
Problem 5-4)
Capacitors and inductors
a) Capacitors and inductors are circuit elements with a frequency independent impedance
b) Inductors cannot be used to make filters
c) To make integrator as well as differentiator circuits, one has to use both inductors and
capacitors
d) A capacitor blocks ac signals
e) An inductor has only ohm resistance for dc signals
Problem 5-5)
AD and DA converters
a) A DA converter converts an analogue signal to a digital signal
b) An AD converter can only convert voltage-based signals and not current based signals
c) An analogue signal has theoretically infinitely high resolution
d) If a DA converter is connected after an AD converter, the resolution of the analogue
signal after the DA conversion equal the resolution before the AD conversion
e) A DA converter always require a clock signal in order to operate