ANSWERS

CH. 26: 4, 16, 19, 28, 31, 43, 44, 46, 48, 49

QUIZ  7, CHAPTER 26 PROBLEMS 

Simulation: Click here for the motion of an electron in a uniform electric field.

4. Internal resistance is often  given the symbol r, a small case letter to suggest it is small.  See fig.  26-1 and related discussion. Terminal  voltage is defined to be Vab = ε - i*r (eqn. 26-1) , where ε is the voltage across the battery when no current flows. i.e. when i = 0.  In the case at hand, you are given ε = 12.0 (V). You are also given i and  Vab.  Find r.

16. See class notes.  Convert the 820 ohm and 680 ohm resistors into a parallel  equivalent given by Rp = (680)*(820)/(680 + 820)  ohms. Then evaluate the sum Rp + 960 ohm  for the effective series connection.
19. See class notes.  Convert the two  identical  resistors in series into one resistor of value 2R. Note   2R is parallel  with R;  the parallel equivalent of these is  (2/3)*R.

Now find the equivalent resistor of the above-mentioned  resistors in the part of the circuit above the R between point A and  C.   This equivalent resistor is
R + (2/3)*R = 1.67*R;  this  resistor is parallel with the  R between point A and  C and is given by (1.67*R*R)/(1.67R + R). Add this last expression to R in order to compute the total equivalent resistor between points A and C. 
28. Find the total current by  using Kirchoff's second rule or loop rule,  page 684. You will discover the 
current i flows clockwise around the circuit. Then  find 18 (V) - i*r2   and 12(V) + i*r1.  In the last expression ,  we add because the change across the battery and  internal resistor have the same sign.
31. This is a good one.    At junction a, I1 + I2 - I3 = 0.  For the rest , see example 26-9. 
43. See example 26-14, dealing with turn signals. Both turn signals and windshield  wipers involve  repetitive motions based upon  alternate charging and discharging.  A typical turn signal flashes perhaps twice per second and a typical windshield  wiper wipes once per second up or down. 
44.
(a) RC = 24x10-6 seconds; find C given R.
(b) Use equation 26-6a  for the charge on the positive plate of the  capacitor. Q = C*E(1 - e-t/RC), where E = 24.0 (V). The voltage across the resistor has magnitude I*R.  To get I , differentiate the expression for Q: I = dQ/dt. You will get a decaying exponential of the form Io*e-t/RC. Note Io = E/R. Thus,  I*R = E*e-t/RC , where E = 24.0 (V). Find the time it takes I*R to decrease from 24.0 (V) to 16.0 (V)
more discussions to come!