1- Find the equivalent resistance for the circuit in the figure. (Use the following as necessary: V_emf, R.)

2- The dead battery of your car provides a potential difference of 9.630 V and has an internal resistance of 1.150 Ω. You charge it by connecting it with jumper cables to the live battery of another car. The live battery provides a potential difference of 12.00 V and has an internal resistance of 0.0100 Ω, and the starter resistance is 0.0700 Ω. (a) Draw the circuit diagram for the connected batteries. (The starter is in parallel with the live battery.) (Do this on paper. Your instructor may ask you to turn in this work.)

(b) Determine the current in the live battery, in the dead battery, and in the starter immediately after you closed the circuit.

3- The circuit shown in the figure consists of two batteries with V_A = 6.3 V and V_B = 12.1 V and three light bulbs with resistances R₁, R₂, and R₃. Calculate the magnitudes of the currents i₁, i₂, and i₃ flowing through the bulbs.

4- A circuit consists of two 3.45-kΩ resistors in series with an ideal 12.0-V battery. (a) Calculate the current flowing through each resistor. (b) A student trying to measure the current flowing through one of the resistors inadvertently connects an ammeter in parallel with that resistor rather than in series with it. How much current will flow through the ammeter, assuming that it has an internal resistance of 2.5 Ω?

5- What is the time constant for the discharging of the capacitors in the circuit shown in the figure? If the 2-µF capacitor initially has a potential difference of 63 V across its plates, how much charge is left on it after the switch has been closed for a time equal to half of the time constant?

6- A 6.0-V battery is attached to a 6-mF capacitor and a 440-Ω resistor. Once the capacitor is fully charged, what is the energy stored in it? What is the energy dissipated as heat by the resistor as the capacitor is charging?