Two resistors, R1 and R2, are connected across an ideal battery of emf E (internal resistance negligible). Consider two separate arrangements: (A) the resistors are connected in series, and (B) they are connected in parallel.
(i) For arrangement (A), prove that the power dissipated in each resistor is directly proportional to its resistance.
(ii) For arrangement (B), prove that the power dissipated in each resistor is inversely proportional to its resistance.
(iii) If R1=6Ω, R2=3Ω, and E=12V, calculate the power developed in each resistor for both arrangements.
(iv) Compare the total power drawn from the battery in the two arrangements and comment on the result.