Three resistors of values 2Ω, 4Ω and 6Ω are given to a student.
(a) Without performing any numerical calculation, state which arrangement—series or parallel—of these three resistors will produce the largest equivalent resistance. Give a reason for your answer.
(b) Without calculation, state which arrangement of the three resistors will produce the smallest equivalent resistance. Give a reason for your answer.
(c) Consider the following three arrangements:
(i) the 2Ω and 4Ω resistors connected in series, and this combination connected in parallel with the 6Ω resistor;
(ii) the 2Ω and 4Ω resistors connected in parallel, and this combination connected in series with the 6Ω resistor;
(iii) all three resistors connected in parallel.
Rank the equivalent resistances of these three arrangements from highest to lowest, giving qualitative justification in each case.