Incredibly annoying question which I just don't know how to approach. (may be hard to convey without the diagram, but I'll try. I have written solutions to the questions I have already completed.)
a) A cell of emf

and internal resistance r is connected in series to a resistor of resistance R as shown. A current I flows in the circuit.
(Shows standard series circuit with said components.)
i) State an expression which gives

in terms of I, r, and R.
Answer:

ii) Hence show how

, the p.d. across the resistor, is related to

, I and r.
Answer:
b) A lamp, rated at 30W, is connected to a 120V supply.
i) Calculate the current in the lamp.
Answer:

ii) If the resistor in part (a) is replaced by the lamp described in part (b), determine how many cells, each of emf 1.5V and internal resistance 1.2

, would have to be connected in series so that the lamp would operate and its proper power.
Attempt at answer:
R of lamp =






Number of cells =

, which is quite clearly a ridiculous figure, so there must be a hole in my understanding somewhere... would anybody care to fill it? This question has been getting at me all day long.
