A resistor made from a wire of length L, cross sectional area A is connected to an ideal battery. (a) If we double the length of the wire (leaving the area, wire's material composition, and the battery as it was originally,) what happens to each of the following quantities? Recall the voltage across the resistor stays constant because it is connected directly to an ideal battery! . Does the current through the wire increase, decrease, stay the same, or is there insufficient information? • Does the current density in the wire increase, decrease, stay the same, or is there insufficient information? • Does the power dissipated in the wire increase, decrease, stay the same, or is there insuffi- cient information? • Does the electric field in the wire increase, decrease, stay the same, or is there insufficient information? . Does the density of the charges in the wire increase, decrease, stay the same, or is there insufficient information? (b) if we instead double the radius and therefore the cross sectional area of the wire increases by a factor of 4 (leaving the length, wire's material composition, and the battery as it was originally,) what happens to each of the following quantities? . Does the current through the wire increase, decrease, stay the same, or is there insufficient information? . Does the current density in the wire increase, decrease, stay the same, or is there insufficient information? • Does the power dissipated in the wire increase, decrease, stay the same, or is there insuffi- cient information? . Does the electric field in the wire increase, decrease, stay the same, or is there insufficient information? . Does the density of the charges in the wire increase, decrease, stay the same, or is there insufficient information?

In the figure the ideal batteries have emfs &₁ = 18.8 V, &2 = 9.08 V, and 3 = 5.40 V, and the resistances are each 2.20 2. What are the (a) size and (b) direction (left or right) of current i₁? (c) Does battery 1 supply or absorb energy, and (d) what is its power? (e) Does battery 2 supply or absorb energy, and (f) what is its power? (g) Does battery 3 supply or absorb energy, and (h) what is its power? #H (a) Number i (b) (c) 1 & 3. (d) Number (e) (g) left i (f) Number i supply [ supply (h) Number i Units #1&₂ A Units W Units W Units W

Your flashlight is getting dimmer and dimmer, so you assume the batteries are nearly dead. They are “D” cells producing 1.5 volts. You take the batteries out and test them with a voltmeter. The meter reveals the batteries have nearly 1.5 volts of potential. Are the batteries dead or is something else going on? Discuss how you can tell whether the batteries are dead, and how you would test the flashlight to see whether there is some internal problem. Is it an either-or proposition? Explain.

The resistances in Figure (a) and Figure (b) are all 8.7 Q, and the batteries are ideal 28 V batteries. (a) When switch S in Figure (a) below is closed, what is the change in the electric potential V, across resistor 1, or does V, remain the same (enter "O")? (b) When switch S in Figure (b) below is closed, what is the change in V1 across resistor 1, or does V1 remain the same (enter "0")? R3 R1 R2 R1 R2 (a) (b) (a) Number i Units (b) Number i Units

Two circuits are shown below, each consisting of a battery and one resistor. The batteries are ideal and identical, supplying 2V to the circuit. The cylindrical resistors are made of the same material but have different sizes. Resistor R1 is 1cm long and has a diameter of 0.025cm while resistor R2 is 1.75cm long and has a diameter of 0.01cm. (Note, Plane P has no effect on the circuit and is a fictitious electron counter) A. If the current through R1 is measured to be 0.4211A, what is the resistivity (p) of the material that the resistors are made from? Plane P 2V Circuit-1 B. What is the resistance of R2 and what is the battery current for circuit-2? [if you are unable to do part A, assume p 1.5x10-6Q-m] 2V Circuit-2 C. If R1 and R2 were placed in series as shown, how much power is dissipated by each resistor? R2 2V

In the circuit below, all four resistors are identical (R, = R2 = R3 = R4 = R) and the battery has a voltage of 5.06 V. R1 R2 V R3 R4 (a) When the switch is placed in position 1, the measured current in the battery is 1.2 mA. What is the value of each resistor? kΩ (b) When the switch is placed in position 2, what is the current flowing out of the battery? (c) When the switch is open (neither in position 1 or position 2), what is the current flowing out of the battery?