Dividing Dividers

The questions below are due on Monday September 16, 2024; 10:00:00 PM.
 
You are not logged in.

Please Log In for full access to the web site.
Note that this link will take you to an external site (https://shimmer.mit.edu) to authenticate, and then you will be redirected back to this page.

1) Half?

Consider the following circuit, which is designed to use two resistors to cut a 10{\rm V} voltage drop in half:

Solve for the voltage v_o in the circuit above, in Volts.

v_o =~

2) Quarter?

Now consider taking the circuit from the previous part and hooking up two more 1{\rm k}\Omega resistors to cut that voltage in half:

Solve for the voltage v_o in the circuit above, in Volts.

v_o =~

3) Quarter?!

It didn't work!!! But it turns out that it is possible to use a circuit of a similar form to cut a voltage by a factor of 4. For the rest of the problem, we'll explore three different ways we could accomplish this.

Let's start with our original configuration containing only two resistors, but now with one resistance unspecified:

Find a value of R (in Ohms) so that v_o=2.5{\rm V} in the circuit above. If no such value exists, enter None instead.

R =~

4) Quarter?!?!

Now let's move back to our four-resistor configuration. Here our goal is to pick the resistor values R_1 and R_2 so that the v_o is 2.5{\rm V}.

Let's first consider the case when R_1 is replaced with a wire (i.e., R_1 = 0\Omega). In this case, what value of R_2 makes v_o = 2.5{\rm V}? Enter a single number in the box below, representing the resistance of R_2, in Ohms:

R_2 =~

5) Quarter?!?!?!

Now, let's consider the same circuit, but in the case when R_1 is about the same size as the 1{\rm k}\Omega resistors in the circuit. That is, let's assume that R_1 is between 100\Omega and 10k\Omega. Under this constraint, what are values of R_1 and R_2 that make v_o = 2.5{\rm V}?

Enter your answer as as Python list containing two numbers [r1,r2], where r1 is the value of R_1 in Ohms, and r2 is the value of R_2, also in Ohms. Note that there may be multiple correct answers. Any correct answer will be accepted.
 
[R_1, R_2] =