Kirchhoff’s Rules Physics 102 Professor Lee Carkner Lecture 15

PAL #14 Ohm’s Law  1.5 V battery, 167 A current in 1 m long, 2 mm thick wire  R = V/I = 1.5/167 =   R =  (L/A)   = RA/L = ( )(p)(0.001)2/1   = 2.8X10 -8 (  m)  wire is aluminum  “The relationship R = V/I tells us that the resistance of a wire is directly proportional to the potential difference applied to it.”  false    Appling a potential difference V will produce a current such that R = V/I, but changing V changes I not R

The current in a wire has a direction to the right. What direction is the flow of electrons and the electric field in the wire? A)Right, right B)Left, left C)Right, left D)Left, right E)We 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 

Circuit Rules  Series:   Current:  Voltage:  Resistors: R eq = R 1 + R 2 + R 3 …  Parallel   Current:  Voltage:  Resistance: 1/R eq = 1/R 1 + 1/R 2 + 1/R 3...

Resistance  Each resistor just has a resistance R   Series: add resistors to get larger equivalent resistance   A plain wire is assumed to have no resistance

Magnitude of V, R and I  When is current large?   In parallel, branches with larger R have smaller I (I =  V/R)  When is voltage large?   In parallel, voltage is all the same, so each branch has the same amount of energy   For complicated circuits we will apply the conservations laws through Kirchhoff’s Rules

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  The sign of the potential change depends on the direction you traverse the loop  Batteries   When moving from + to - terminal the  V is equal to –V   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 … )  3.Use the junction rule for each unique junction 4.Use the loop rule for each loop  5.Solve for each variable via substitution 

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 VV V2V2 V3V3 I1I1 I2I2 I3I3

Today’s PAL  Solve for the current and potential difference through each resistor and battery by using Kirchhoff’s rules + -  V = 6 V 6   4 

Dangerous Currents  The current that flows through household wires is dangerous in two ways    Currents of a few tenths of an amp can cause severe burns or muscle paralysis  Electrical devices and power connections are designed to minimize these risks

Household Power   A fuse is a device designed to break the connection if the current through it exceeds a certain value   Each outlet has connections to two wires:   A ground wire at 0 V   For larger appliances, a second line at -120 V is installed  The potential across this line and the normal +120 V line is 240 V

Electrocution   A lack of insulation produces a “live” wire   Another danger is a “short circuit”   The path of least resistance is through you to the ground 

Next Time  Read Ch  Homework, Ch. 19, P: 20, 27, 29, 35