Solve the following questions given below:

Question I: Derive a formula for the current through a circuit consisting of a single bulb with resistance R and an ideal source of emf, providing a voltage. What is the power of this bulb?

Question II: Now construct a parallel circuit consisting of 2 identical bulbs of resistance R each supplied by the same voltage source. What is the equivalent resistance of this circuit, the current through the source and the current through each bulb? What is the power per bulb in this case? How does it compare to that of the single bulb circuit?

Question III: Construct a parallel circuit consisting of 3 identical bulbs with resistance R each and the ideal source of voltage used for parts a) and b). Again, calculate the equivalent resistance of this circuit, the current through the source and the current through each bulb, as well as the power per bulb. How do your answers compare with those of part a) and b)? Explain your findings.

Question IV: Redo the work above using a real source of emf with the internal resistance r. Make sure to draw the circuits and label them with all needed quantities.

Show all work, use additional paper if necessary.