UNIVERSITY PHYSICS II
UNIVERSITY PHYSICS II PHYS 2044
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This 6 page Class Notes was uploaded by Maverick Braun on Friday October 2, 2015. The Class Notes belongs to PHYS 2044 at Arkansas State University taught by Staff in Fall. Since its upload, it has received 23 views. For similar materials see /class/217733/phys-2044-arkansas-state-university in Physics 2 at Arkansas State University.
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Date Created: 10/02/15
PHYSICS II Kirchhoff s Rules Objective Practice in reading schematic diagrams connecting circuits using electrical meters and experimental tests of Kirchhoff s Rules LAM 21599 Apparatus Heath Power Supply DVM lOOOQ xed resistor in a small wood box two decaderesistance boxes DPDT switch connecting wires Theory Two of the fundamental laws of physics involve conservation of charge and conservation of energy Kirchhoff made use of these laws in devising a procedure for writing a system of equations that can be solved to obtain the currents in a complex electrical network In the network shown in Figure l the charge must be conserved at each branch point a branch point is any point where three or more conductors join Thus at branch points a and b Kirchhoffs First Rule states since the total current owing in must be the same as the total current owing out Sum of currents in Sum of currents out or Sum of currents in Sum of currents out 0 or for point a 1211130 and for point b 11I3120 where the directions of 11 12 211K113 were chosen arbitrarily If any direction is chosen wrong that current value will be negative when the mathematical system of equations is solved Figure 1 Simple circuit for application of Kirchhoffs Rules Note that equations 1 and 2 are identical In general if there are n branch points only 11 1 independent current equations may be written For any closed path or loop in the circuit of gure 4 energy gains and losses must be the same Thus for any closed path Kirchhoff39s Second Rule states Sum ofthe EMF s Sum ofthe IR losses or Sum of potential gains Sum of potential losses 0 For the top rectangular loop starting clockwise at point a 131 v1 v2 0 3a 01 131 R111 R212 0 3b and for the bottom rectangular loop starting clockwise at point b v3 E3 v2 0 4a 01 11313 E3 R212 0 4b Another equation may be obtained by starting clockwise at point a around the outside rectangular loop as E1V1V3E30 5a 01 E1 R111 R313 E3 0 5b However equation 5 is not independent but is the sum of equations 3 and 4 In general application of Kirchhoff39s Rules requires a Label the voltage sources b Choose and label an arbitrary current direction in each distinct path in the network for a total of N unknown currents b Indicate polarities for each circuit component c Write n 1 current equations for the network containing n branches d Write N n 1 independent voltage equations for the network e Solve the system for the N unknown currents Equations 1 3b and 4b may be solved using Cramer s Rule to yield 11 E1Rz R3 E3RzD 6 12 E1R3 E3R1D 7 I3 E3R1 R2 E1R2D 8 where DR1R2 R1R3 R2R3 Procedures Before connecting the circuit turn on the power supply and adjust output A to 10 vols amp then turn off the power supply Also set the decade box values to R15OOQ amp R3800 2 and use the ohm scale of your DVM to carefully measure Rl R2 amp R3 generally your FLUKE DVM is more accurate than the decade boxes Then turn off the power supply and connect the circuit as in Figure 2 carefully observing polarities Have your instructor check your connections Use the 5V supply and output A gt Do Not use output B it won39t work in this circuit Note The xed 10009 resistor R2 is only within 5 of stated value you must use the measured values in the calculations r Output A Set to 10 v 3 Volts 8009 Figure 2 Kirchhoffs Rules Experimental Circuit 2 Turn on the power supply close the switch and measure V10 V5 this may not be exactly 5V V500 V1000 and V300 Record these values with their polarities on a circuit diagram like Figure 5 9 Open the switch and turn off the power supply 4 Check to verify that energy is conserved by verifying equations 3a and 4a Kirchhoff 5 Second Rule Notify your instructor if you have trouble 5 Compute 1500 11000 and 1300 by Ohm39s Law I VR amp actual R values and show that Kirchhoffs First Rule is satisfied Equation 1 and Equation 2 6 Use equations 6 9 to solve for the theoretical values of 1500 11000 and 1300 Compare and comment on the two sew of values for the 139s Note that the multimeter is i l2 and the connecting wire resistance is negligible Your report should include schematic diagram with all values experimental calculations and a concluding paragraph on sources of error and other comments about this experiment Problems 345 3417 3415 3417 34131 3215 3217 3211 32153 32147 32151 Students Wishing to not take the nal exam must turn in the underlined problems to me before Wednessdayi If the quality of the homework is not suf ciently high they Will not be exempt Inductance o For a typical coil the current in changing the resulting B eld is changing the changing B eld produces a changing magnetic ux and a changing magnetic ux produces a voltage known as the back em d1 6 7L a 1 The inducance in any coil is N 39i39 B L 7 7 lt2 Where B is the magnetic ux through the coil for a xed current and N is the number of turns 0 For an ideal solenoid the inductance is L 3 Here N is the the number of turns A is the cross sectional area Z is the length of solenoidi You should be able to derive this result 7 140N214 7 Z 0 The Energy stored in an inductor is U 1L1 4 2 The energy is stored Within the magnetic eld The energy per unit volume is B2 u 5 B 2 0 LC circuits 7 In an L C circuit that has zero resistance the current and charge on the capacitor change as Q Qmaxcosmmb lt6 I ionmaxsinwm a5 7 dt W Imax Where Qmax is the maximum charge on the capacitor and W0 8 is the oscillation frequency of the circuit 7 The energy in the LC circuit is constant and is the energy stored in the 1 1 2 U7 L1t2 C 9 Note at certain moments there is no current and only charge At other moments there is only current and no charge so Q33 10 Waves 0 1n free space the electric eld and magnetic eld obey the wave equation 82E 8E w My 11 82B BB w My 12 o The solution to this equation is E Emax coskz 7 wt 13 B Bmax coskz 7 wt 14 With 27f k7 w27rf cf 15 o The magnitude of the electric eld and the magnitude of the magnetic eld are related E CB 16 o The waves travel With the speed of light 5 Where 1 C 7 17 xMDED 0 Electric eld and magnetic eld are perpendicular to the direction of propogationi If you take your right hand and curl your ngers from E to B your thumb points in the direction of propogationi Below S points in the direction of propogationi E B o The magnetic energy per volume stored in the wave is the same as the electric energy per volume stored in the wave B2 7 2 1 w EEO E2 m 18 The total energy per volume in the wave is uuEuB 19 o The energy crossing a surface per unit area per unit time is given by the Poyting vector 1 s 7E X B 20 M0 The direction of the Poyting vector is in the direction of propogationi 0 Usually the amplitude of the light is oscillating very fast and over short distances7 nanometers and 1015H2 for visible light It therefore makes sense to de ne the average pointing vector and average energy density etc 7 For instance uEgt lt eDE2tgt lt eoE lax cos2kz 7 wtgt ieoEglax 21 7 Similarly lt gt 1 32 22gt uB 7 4M0 max 7 The average magnetic and average electric energies are equal ltuBgt um 23 7 The total energy per unit volume is 1 1 lutocl WE uBgt i oEglax 331 24 7 The average rate of energy ow per unit area per unit time is ltSgt ltumgt c 25 Emameax 26 2M0 7 The momentum per area per time also known as pressure carried by the light wave is P 7 27 C lt gt If the light is completely absorbed then this amount of momentum per area per per time is transfrered to the absorbing object If the light is totally re ected then the light comes in With this amount of momentum and goes back With this amount of momentum the amount of momentum change per area per time is S P 22 28