Simple Nature - Light and Matter

knob turned all the way clockwise, the variable resistor’s resistance isnearly zero, and when it’s all the way counterclockwise, its resistanceis essentially infinite.) (a) Draw schematics. (b) Why would thesimpler design be undesirable?23 You have a circuit consisting of two unknown resistors inseries, and a second circuit consisting of two unknown resistors inparallel.(a) What, if anything, would you learn about the resistors in theseries circuit by finding that the currents through them were equal?(b) What if you found out the voltage differences across the resistorsin the series circuit were equal?(c) What would you learn about the resistors in the parallel circuitfrom knowing that the currents were equal?(d) What if the voltages in the parallel circuit were equal?24 How many different resistance values can be created by combiningthree unequal resistors? (Don’t count possibilities in whichnot all the resistors are used, i.e., ones in which there is zero currentin one or more of them.)25 Suppose six identical resistors, each with resistance R, areconnected so that they form the edges of a tetrahedron (a pyramidwith three sides in addition to the base, i.e., one less side than anEgyptian pyramid). What resistance value or values can be obtainedby making connections onto any two points on this arrangement?⊲ Solution, p. 93726 A person in a rural area who has no electricity runs anextremely long extension cord to a friend’s house down the road soshe can run an electric light. The cord is so long that its resistance,x, is not negligible. Show that the lamp’s brightness is greatest ifits resistance, y, is equal to x. Explain physically why the lamp isdim for values of y that are too small or too large.27 All three resistors have the same resistance, R. Find the√three unknown currents in terms of V 1 , V 2 , and R.Problem 27.548 Chapter 9 Circuits