Series and parallel resistors Kirchhoff’s Rules for network problems Electrical meters and household circuits DC CIRCUITS: Chapter 26 C 2009 J. F. Becker

DIRECT-CURRENT (DC) CIRCUITS In this chapter we will study methods of analyzing more complicated circuits having several sources, resistors, and other circuit elements. In general, we will find the current and power dissipation in each circuit element. First we consider ways to simplify resistors connected in a circuit in series and parallel. Second we consider Kirchhoff’s two rules to simplify more complicated networks. C 2009 J. F. Becker

Series connection Parallel connection Resistors connected in a circuit in series or parallel can be simplified using the following:

Method of simplifying the circuit in (a) below to get the equivalent resistance. We can then calculate the power P = I 2 R dissipated in each resistor.

Ch. 26 #11: Four equivalent light bulbs R 1 = R 2 = R 3 = R 4 = 4.50 , emf = 9.00 Volts. Find current and power in each light bulb. Which bulb is brightest? Later, if bulb #4 is removed which bulbs get brighter? Dimmer?

On course website, see old Test #1 from semesters S-04, F-03, and others for typical DC circuit problems, AND other typical problems on tests… C 2009 J. F. Becker

These complex circuits cannot be reduced to series – parallel combinations. So use Kirchhoff’s Rules:  I j = 0 (junction rule, valid at any junction); conservation of charge  (  V j ) = 0 (loop rule, valid for any closed loop); conservation of energy

Use Kirchhoff’s junction rule at point “a” to reduce the number of unknown BRANCH currents from three to two.

ELECTRICAL MEASURING INSTRUMENTS – METERS A d’Arsonval galvanometer meter movement:

AMMETERS have a very small shunt resistor in them to reduce the effect of introducing the meter resistance into the circuit being measured. VOLTMETERS (  V ) have a very large series resistor in them to reduce the amount of current drawn from the circuit being measured.

House wiring circuits

Hand drill circuit with ground wire for safety

Note: Section 26.4 Resistance-Capacitance (RC) Circuits will be deferred until later Next, back to the second half of Chapter 21: Chapter 21 Electric Field and Coulomb’s Law and Vectors Chapter 22 Gauss’s Law Chapter 23 Electric Potential Chapter 24 Capacitance and Dielectrics C 2009 J. F. Becker

See Review C 2009 J. F. Becker