Sample quiz 6 questions

This is a sample quiz and need help trying to use it as a source for a study guide for the upcoming quiz please show your work 

ECE115, Quiz #5, F/12 Score________

Name ______________________________ Lab Sect _____________

1) The input voltage to an amplifier is ( ) 3 cos (100 / 12)inv t tπ π= − , and the output voltage is

( ) 12 cos (100 / 4)outv t tπ π= − . What is the gain G of the amplifier?

2) The current through a 5 Fµ capacitor is ( ) 0.5 cos (4000 / 4)i t t π= − .
a) What is the current phasor I ?

b) What is the capacitor impedance?

c) What is the phasor V of the voltage across the capacitor?

d) What is the voltage ( )v t across the capacitor?

3) The frequency 0ω of a signal 0( ) 0.5 cos( )x t tω= varies over the range 00 2 (10000)ω π≤ ≤ .
a) In Hz, what is the bandwidth of the signal ( )x t ?

b) Consider the signal ( ) (0.5 ( )) cos(2 (720000) )y t x t tπ= + . What is the frequency range in Hz

of the sinusoids that are in the signal ( )y t ? Hint:
1

cos( ) cos( ) (cos( ) cos( ))
2

α β α β α β= + + − .

4) The voltage source is ( ) 12 cos ( )v t tω= . In the circuit shown below, where 1 4R K= Ω ,
0.05C Fµ= and 2 3R K= Ω .

a) What does the amplitude of the voltage ( )Cv t become as 0ω → ?

( )v t ( )Cv tC2R

1R( )i t

b) What does the current ( )i t becomes as ω → ∞ ?

5) In terms of the logic variable inputs a, b, and c, give a Boolean function for the output y =
f(a,b,c) of the circuit shown below.

a
b

y
c

6) Complete each of the following logical expressions.

a) x + 1 = _____ , b) x + 0 = _____ , c) x  x’ = _____ , d) x + x = _____ , e) x + x’ = _____ ,

f) x  0 = _____ , g) x  1 = _____ , h) x  x = _____

7) De Morgan’s Theorem is given by: a) (a  b)’ = a’ + b’ and b) (a + b)’ = a’  b’.

Prove version (a) of De Morgan’s Theorem.