Question

Can someone show me how the double-throw switch works in this problem?

Answer 1

So in the attached file, there are three states in which the current shows.

1) The switch is as show (open)
2) The switch is at position 1
3) The switch is at position 2

The solution yields that:
1) When the switch is open, the resistance in the circuit is $$ R1 + R2 + R3 $$
2) When the switch is at position 1, the resistance in the circuit is $$ R1 + (\frac{1}{R2} + \frac{1}{R2})^{-1} + R3 $$
3) When the switch is at position 2, the resistance in the circuit is $$ R1+ R2 $$

Answer 2

So this is how I imagine the current in each state (open, 1, 2). Is this correct?

Answer 3

If it is correct ..... why?

Answer 4

Path of least resistance or something?

Answer 5

The easiest way to do this (and how I'm doing it right now) is just to set up 3 different circuits. One circuit with the switch in each of it's positions. Find the equivalent resistances for each circuit, in terms of R1, R2, R3. Then plug in the different information you are given to the corresponding circuit, and find the value of the equivalent resistor in terms of voltage and current.

This will give you 3 equations, and you need to find 3 variables.

If this doesn't make sense, we can go one step at a time :)

Answer 6

Going step-by-step would actually really help. I'm good with R/C & RC circuits, but switches always confuse me.

Answer 7

It's more or less, I don't know how to draw the switch, or which way the current flows once it's switched.

Answer 8

Oooh, I see your confusion. It's not very clear where the switch "pivots" around. Let me double check that I did it correctly :)

Answer 9

Exactly!

Answer 10

So, I'm pretty sure that the switch is supposed to turn in this manner:
Position 1:

Position 2:

Open:


If that makes any sense (can't figure out colors to differentiate the switch from the rest)