Two flashlight batteries in series power a circuit consisting of four ohmic resistors as shown, connected by copper wires
with negligible resistance. The internal resistance of the batteries is negligible. Two magnetic compasses are placed
underneath the wires, initially pointing northward before closing the circuit. A very-high-resistance voltmeter is connected
as shown in Figure 20.80.
(a) Starting from fundamental principles, write equations that could be solved to determine the conventional current
through each resistor, and show the directions of these currents on the diagram. Explain where each of your
equations comes from. Do not use formulas for parallel and series resistances (but you are free to use such formulas
to check your work if you like). If these equations are solved, we find that the current through R1 is 0.073 ampere
and the current through R4 is 0.102 ampere.
(b) Sketch the positions of the compass needles. Compass 1 deflects by 3 degrees. What is the deflection angle of
compass 2?
(c) The resistors are made of a material that has 8 × 1028 free electrons per cubic meter and a mobility of 3 × 10−5
(m/s)/(N/C). Find E2, the magnitude of the electric field in resistor R2, which is in the form of a short wire with a
constant cross-sectional area of 6 × 10−10 m2.
(d) Is the field E1 in resistor R1 larger, smaller, or the same as E2?
(e) What is the length of resistor R2?
(f) What does the voltmeter read, including sign?
(g) How much energy in joules is expended by the batteries in moving a singly charged ion from one end of one of the
batteries to the other end of that same battery?
(h) How much power output is there from one of the batteries?