The best thing you can do inorder to solve these kind of question is; assign potential across resistor logically.
- Resistor having same potential difference across them are in parallel.
- Otherwise, in series.
Caution: Always first solve series and replace the whole series resistor with one resistor of effective resistance you measured and then go to calculate for parallel one.
Assume emf of battery to be anything like say, 'V'. So say positive terminal have potential V and negative have 0. So for the first case, as both the resistor have same P.D. V across them, hence they are in parallel. For second case, same thing we do but for R3 there will be a potential drop across it ( as we know there is always a potential drop across a resistor, if current flows through it) let say its 'x'. Therefore
1. PD across R1, 'x'
2. PD across R2, 'x'
3. PD across R3, 'V-x'
So, R1 and R2 are in parallel, where as R3 in series. So add R1 and R2 as parallel and then add the resulting effective resistance in series with R3.