Simple Circuits PH 203 Professor Lee Carkner Lecture 12

Batteries   Stands for electromotive force   For a real battery there is internal resistance (r) so the potential is:  – ir

Junction Rule  The sum of currents entering a junction is equal to the sum of currents leaving it   You need to define a magnitude and a direction for the current in every unique piece of the circuit   You can apply the junction rule to every junction

Loop Rule  The sum of the potential differences around a closed loop must be zero   Since you wind up back where you started from all of the changes in energy must cancel out   A loop is any closed path the current can flow through

Loop Rule Conventions   Batteries  When moving from - to + terminal the  V is equal to +   When moving from + to - terminal the  V is equal to –    Resistors   When moving against the current the  V is +iR

Using Kirchhoff’s Rules 1.Find junctions and mark with big dot  2.Draw the direction and assign a variable to all currents (i 1, i 2, i 3 … )   Each part of a circuit that is between two junctions has its own current 3. 4.Use the loop rule for each loop  5.Solve for each variable via substitution  You need as many equations as you have variables

Example  Junction rule:   Loop rule:    If you knew all of the  ’s and R’s you could solve for the i’s R1R1 R2R2 R3R3     2 2  3 3 i1i1 i2i2 i3i3

Resistors in Series  All resistors in series have the same current (i)   Since  V eq is the sum of all the individual  V, R eq must be the sum of all of the individual R:  R eq = R 1 + R 2 + R 3 …  Resistors in series add  V eq R1R1 R2R2 i

Resistors in Parallel  All resistors in parallel have the same  V   Since the current through each is i =  V/R and i eq =  V/R eq :  V/R eq =  V/R 1 +  V/R 2 1/R eq = 1/R 1 + 1/R 2 + 1/R 3... VV R1R1 R2R2 i eq i1i1 i2i2

Magnitude of V, R and i  When is current large?  In series, each resistor has the same current, so fewer total resistors means larger current   When is voltage large?  In series resistors with larger R have larger  V (larger potential drop,  V = iR) 

Next Time  No class this Friday or next Monday  No lab this Thursday  Read  Problems: Ch 27, P: 16, 17, 22, 70, 74

A material is said to obey Ohm’s law only if A)For any given voltage we can write V =iR B)The material is a semiconductor C)The material is a metal D)The plot of voltage versus current is a straight line E)The drift speed of electrons is very low

Consider three light bulbs, 30 W, 60 W, and 100 W, which has the highest resistance if hooked to household current? A)30 W B)60 W C)100 W D)All tie E)You cannot tell from the information given

If the voltage applied to a resistor is doubled, what happens to the current and power? A)Double, double B)Quadruple, quadruple C)Double, quadruple D)Quadruple, double E)We cannot tell from the information given

A 100 W light bulb is connected to 120 V household current. What is its resistance? A)1.2  B)100  C)144  D)200  E)12000 