a. A set of batteries and bulbs are connected as shown in the figure at the right. All of the bulbs have resistance R and the current through bulb C is I as indicated. Use Kirchoff's laws to find:

• the current through bulbs A and B and through the battery
• the voltage drop across the battery.

Express your answers in terms of R and I. In explaining your argument, explain which of the Kirchoff principles you are using and how. If you have not used all of them, discuss whether you are using the missing ones implicitly or whether they are not relevant here.

b. An electrical circuit is connected as shown in the figure on the right.   It contains two identical batteries. The battery labeled #1is rated at 6 Volts and the one labeled #2 is rated at 3 Volts. The 3 bulbs (labeled A, B, and C) are identical and, at the currents in the circuit, each bulb can be taken to have almost a constant resistance of 3 Ohms. Use Kirchoff's laws to find:

• the current through each of the bulbs and
• the current through each of the batteries.

In explaining your argument, explain which of the Kirchoff principles you are using and how. If you have not used all of them, discuss whether you are using the missing ones implicitly or whether they are not relevant here.