Five identical resistors are connected to a cell as in the diagram. The potential differences across R1 , R2 and R3 are V1, V2 and V3 respectively. What is the order of increasing potential differences (smallest first)?

Answer:

20) E

Parallel circuits rule: Voltage is equal in all branches.
Hence the two branches of the given circuit must have the same voltage.

Circuits rule: Resistance in series is always greater than resistance in parallel.

In branch 1, the resistors are in series. In branch 2, resistors are in parallel. Hence, branch 1 has more resistance than branch 2.
Since current is inversely proportional to resistance, branch 1 would have less current than branch 2.
Since voltage is directly proportional to current, voltage in branch 1 would be less than voltage in branch 2.
Hence V1 < V2

Branch 2 splits into two more branches. Hence, voltage splits into two more branches.
V2 = ½V3
R2 has double the voltage of R3. Hence, V2 > V3

Compared to R3, R1 has a higher voltage as there are only 2 resistors in branch 1 whilst there are 3 resistors in branch 2.
V1 > V3

Order: V3 < V1 < V2

Hence, E is the answer.