8.5.P8

1. All of the bulbs in the figure at the right have the same resistance R and the battery provides a voltage difference V0. (Most bulbs are brighter when there is more current through them. Assume that is the case for these bulbs.)

a. Draw a copy of this circuit and make a "voltage map", showing the voltage at each point in the circuit. If you have some points at which there is a voltage you do not know, give it a name (e.g., "V₁").

b. Assume that the current through the battery is equal to I (the letter "eye", not the number "one"). Draw a copy of this circuit and make a "current map", showing the current at each point in the circuit. If you have some points at which there is a current you do not know, give it a name (e.g., "I₁").

c. Use Kirchhoff's three principles to generate as many independent equations relating the voltages, currents, and resistances in your maps as you can. Solve for the voltage drops across each of the bulbs and the currents through each of the bulbs and the battery in terms of the given parameters, V₀ and R.

2. Now suppose that bulb B is removed from the circuit. This makes an open circuit through which current cannot pass.

a. What do you expect will happen to the current through bulb A, bulb D, and the battery?  Make this decision before you do any calculations. Explain why you made the choice you did.

b. Now repeat the tasks you carried out in part 1 to solve for the voltage drops across each of the bulbs and the currents through each of the bulbs and the battery in terms of the given parameters, V₀ and R.

c. Did your results agree with your predictions? If you made a correct prediction, do you see how the equations lead to this result? If they do not, do you see what went wrong with your reasoning? Discuss!

Joe Redish 10/16/02 (after the work of L. C. McDermott)