Climbing the Ladder
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In this problem, we'll start taking a look at an interesting circuit that we'll make use of in the week 3 lab (so careful consideration of the circuit here will pay dividends later!). In fact, we'll look at several variants. For each, solve for the indicated voltage. You should use parallel and series resistor reductions, and voltage and current dividers, rather than applying the node method or the brute-force method to the unsimplified circuit. Simplify things down as far as you can; it turns out that each of these networks can be simplified dramatically.
After a while, you may start to notice a pattern; but don't just guess that the later answers follow the pattern! Try to solve things out by hand to see where that comes from.
For each, enter your answer as a Python expression in terms of V (V) and/or
R (R).
1) Circuit 1
2) Circuit 2
3) Circuit 3
4) Circuit 4
