Physics Problems
2a
Homework 08 - Solutions
You need a 45 Ω resistor, but the stockroom has only 20 Ω and 50 Ω resistors. How can the desired resistance be achieved under these circumstances?"
"
A. Put one 50 Ω and one 20 Ω resistor in parallel and then put that combination in series with a 20 Ω resistor." B. Put two 50 Ω resistors in series and then put that combination in parallel with a 20 Ω resistor."
C. Put one 50 Ω and one 20 Ω resistor in series and then put that combination in parallel with a 20 Ω resistor." D. Put two 50 Ω resistors in parallel and then put that combination in series with a 20 Ω resistor.
Let’s analyze each option until we find the right one:
50 Ω
A.
34.29 Ω
20 Ω
=
20 Ω
In parallel you add them in a weird way
1
3
20 Ω
14.29 Ω
2
In series you just add ‘em up! 34.29 Ω
2a cont.
50 Ω
50 Ω
16.7 Ω
B.
=
20 Ω
In series just add them together. 1
3
100 Ω
2
In parallel you do something a little trickier!
20 Ω
C.
50 Ω
20 Ω
15.6 Ω
=
20 Ω
70 Ω
20 Ω
2a cont.
50 Ω
45 Ω
20 Ω
D.
=
50 Ω
1
25 Ω
2
20 Ω
3
45 Ω
Final comments
One way to remember how to add resistors is to take a look how resistance is calculated.
When the resistors are in series, the effective length is increased, but when they are in parallel the effective area is increased."
" ρ is the resistivity of the material: just a constant.
See if you can derive the parallel and series addition laws from the relationship at left assuming all the resistors have the same resistivity. 2b
What can you do if you need a 35 Ω resistor?"
"
A. Put one 50 Ω and one 20 Ω resistor in parallel and two 20 Ω resistors in parallel. Then put these two combinations in series."
B. Put two 50 Ω resistors in series and two 20 Ω resistors in series. Then put these two combinations in parallel." C. Put two 50 Ω resistors in parallel and two 20 Ω resistors in parallel.
Homework 08 - Solutions
You need a 45 Ω resistor, but the stockroom has only 20 Ω and 50 Ω resistors. How can the desired resistance be achieved under these circumstances?"
"
A. Put one 50 Ω and one 20 Ω resistor in parallel and then put that combination in series with a 20 Ω resistor." B. Put two 50 Ω resistors in series and then put that combination in parallel with a 20 Ω resistor."
C. Put one 50 Ω and one 20 Ω resistor in series and then put that combination in parallel with a 20 Ω resistor." D. Put two 50 Ω resistors in parallel and then put that combination in series with a 20 Ω resistor.
Let’s analyze each option until we find the right one:
50 Ω
A.
34.29 Ω
20 Ω
=
20 Ω
In parallel you add them in a weird way
1
3
20 Ω
14.29 Ω
2
In series you just add ‘em up! 34.29 Ω
2a cont.
50 Ω
50 Ω
16.7 Ω
B.
=
20 Ω
In series just add them together. 1
3
100 Ω
2
In parallel you do something a little trickier!
20 Ω
C.
50 Ω
20 Ω
15.6 Ω
=
20 Ω
70 Ω
20 Ω
2a cont.
50 Ω
45 Ω
20 Ω
D.
=
50 Ω
1
25 Ω
2
20 Ω
3
45 Ω
Final comments
One way to remember how to add resistors is to take a look how resistance is calculated.
When the resistors are in series, the effective length is increased, but when they are in parallel the effective area is increased."
" ρ is the resistivity of the material: just a constant.
See if you can derive the parallel and series addition laws from the relationship at left assuming all the resistors have the same resistivity. 2b
What can you do if you need a 35 Ω resistor?"
"
A. Put one 50 Ω and one 20 Ω resistor in parallel and two 20 Ω resistors in parallel. Then put these two combinations in series."
B. Put two 50 Ω resistors in series and two 20 Ω resistors in series. Then put these two combinations in parallel." C. Put two 50 Ω resistors in parallel and two 20 Ω resistors in parallel.