Linear Algebra, 2020a

80 Chapter One. Linear Systems
(c) This is a reasonably complicated network.
3 ohm
3 ohm
9 volt
3 ohm 2 ohm
4 ohm
2 ohm
2 ohm
2 In the first network that we analyzed, with the three resistors in series, we just
added to get that they acted together like a single resistor of 10 ohms. We can do
a similar thing for parallel circuits. In the second circuit analyzed,
20 volt 12 ohm 8 ohm
the electric current through the battery is 25/6 amperes. Thus, the parallel portion
is equivalent to a single resistor of 20/(25/6) =4.8 ohms.
(a) What is the equivalent resistance if we change the 12 ohm resistor to 5 ohms?
(b) What is the equivalent resistance if the two are each 8 ohms?
(c) Find the formula for the equivalent resistance if the two resistors in parallel
are r 1 ohms and r 2 ohms.
3 A Wheatstone bridge is used to measure resistance.
r 1 r 3
r g
r 2 r 4
Show that in this circuit if the current flowing through r g is zero then r 4 = r 2 r 3 /r 1 .
(To operate the device, put the unknown resistance at r 4 .Atr g is a meter that
shows the current. We vary the three resistances r 1 , r 2 , and r 3 — typically they
each have a calibrated knob — until the current in the middle reads 0. Then the
equation gives the value of r 4 .)
4 Consider this traffic circle.
Main Street
North Avenue
Pier Boulevard