Variant 1:
(a)(i) Well, you know that, in series the Resistors have to be added, right? But there you see from A to C, there’s only one resistor, hence the answer R
(a)(ii)B to X, you see that there are two resistors in parallel, which means that you need to use the formula R*R/R+R (or we can use 1/R+1/R=1/Rt) which is equal to R/2.
(a)(iii) From A to Z—you can break it down. A to B, there’s one resistor- R. From B to X- there’s R/2. From Y to Z, there’s only R. Add these three and you’ll get 2.5R.
Variant 2:
(a) when all the switches are open, the resistance is always infinity.
When S1 is open and S2 is closed, two Rs are in series, which means R+R which is equal to 2R
When S1 is closed and S2 is closed, there are two parts there.
One circuit has two resistors in series—making 2R
the other circuit has two resistors is series—making 2R
both these circuits are in parallel with each other, so we use the 2R*2R/2R+2R or 1/2R+1/2R=1/Rt formula for the resistance which gives you just R as the answer.
