Linear Algebra

78 Chapter 1. Linear Systems
parallel pair can be said to be equivalent to a single resistor having a value of
20/(25/6) = 24/5 =4.8 ohms.
(a) What is the equivalent resistance if the two resistors in parallel are 8 ohms
and 5 ohms? Has the equivalent resistance risen or fallen?
(b) What is the equivalent resistance if the two are both 8 ohms?
(c) Find the formula for the equivalent resistance R if the two resistors in parallel
are R1 ohms and R2 ohms.
(d) What is the formula for more than two resistors in parallel?
6 In the car dashboard example that begins the discussion, solve for these amperages.
Assume all resistances are 15 ohms.
(a) If the driver is stepping on the brakes, so the brake lights are on, and no
other circuit is closed.
(b) If all the switches are closed (suppose both the high beams and the low beams
rate 15 ohms).
7 Show that, in the Wheatstone Bridge, if r2r6 = r3r5 then i4 =0. (Thewaythis
device is used in practice is that an unknown resistance, say at r1, iscompared
to three known resistances. At r3 is placed a meter that shows the current. The
known resistances are varied until the current is read as 0, and then from the above
equation the value of the resistor at r1 can be calculated.)