Problem 4 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?

Problem 4 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?