Design a non inverting op amplifier for a voltage gain of 20 and a load of 1 kilo-ohm Determine the output voltage and output op-current if vi=2.02sinwt mA. Answers: R=5 kilo ohms, Rf=95 kilo ohms, vo=2sinwt, io=2.02sinwt mA Solution The non inverting amplifier gain is, Vo/Vi=(1+Rf/Ri) 20=1+Rf/Ri 19=Rf/Ri If Ri=5kohm Rf=19×5kohm=95kohm If output current Io=2.02sinwt mA, then the output voltage is Io=(Vo/1k)+(Vo/Rf) 2.02sinwt m=Vo1.01m Vo=2sinwt V.

1. Design a ruler which can be used to measure all the lenghts from 1 unit to 12 units but this time
put the minimum possible number of marks on the ruler.
Solution
You need at least four marks:
Suppose you had only three marks, located at A inches, A+B inches, and A+B+C inches from
the left edge of the ruler (and that A+B+C+D=12)
Then the possible lengths that could be made would be:
A, B, C, D, A+B, B+C, C+D, A+B+C, B+C+D, A+B+C+D
There are only 10 numbers here, so even if they were all distinct, you couldn't make all the
numbers 1-12
You need no more than four marks:
Put marks at the 1,3,5,11
-|--|--|------|-
1: 1 mark
2: space from 1 to 3
3: 3 mark
4: space from 1 to 5
5: 5 mark
6: space from 5 to 11
7: space from 5 to 12 (edge of ruler)
8: space from 3 to 11
9: space from 3 to 12
10: space from 1 to 11
11: mark at 11
12: whole ruler
Thus, the minimum number of marks needed to be able to make each of the lengths from 1 to 12
is four