DC Circuits Lab Template (Revised) (1) (2)

Figure 2: Logger Pro (V, I) m (slope) = .040 R; Δ m = 24.99 R R = 1/m = 1/.40 = 25R ; Δ R = 1/24.99 = .40R R mean = 24.99 ; % diff = |(25-24.99)/25|*100 = .04% - Based on your data conclude whether the virtual pencil was an ohmic element or not. B. Virtual pencil lead (VP) ρ = 4.2*10^-4 ( Ω∙m ); R VP = 25 Ω D = 0 .6( mm ); Area = piR^2= .2827m^2 L =R*A/P ( m ) = C. Real pencil rod (RP) ρ = 4.2*10^-4( Ω∙m ); D ± ΔD = 2.4 ± .01 ( mm ); L± ΔL = 18 ± 0.1 ( cm ); R RP = 4.2*10^-4(18/pi(0.0024^2) = 4.17 Ω (unit); ∆ R RP = 2.4+0.1 = 12.91 Ω (unit) 3

V emf ( ε battery ) = 8V ( Volts ); Internal resistance R S =4 ( Ω ); R Load (Ω) 1 2 3 4 5 6 7 8 9 10 20 30 40 50 60 I (A) 1.6 1.3 3 1.1 4 1 .89 .80 .73 .67 .62 .57 .33 .24 .18 .15 .13 V Load (V) 1.6 2.6 7 3.4 3 4 4.4 4 4.8 5.9 5.3 3 5.5 4 5.71 6.67 7.06 7.27 7.41 7.5 A = 66.44 (unit); B = 4.098 (unit); ε = √ ❑ = 8.15 V ; % error of ε (with ε battery = 8 V) =1.875% ● From your fit what value of R L maximizes the power in the load? How does it compare to our simulated internal resistance of the battery set to R S = 7 Ω? The internal resistance of the battery is 10Ω The load resistance that maximizes the power in R L = B = 4 ( Ω ) % error of R L (with R S = 4 Ω) = 0% ● Derivation of the condition for a maximum power transfer in a simple DC Circuit .P=I^2R_L dP/dR_L = v_th^2* DISCUSSION & CONCLUSION ( 10 points ): The objective of this lab was to apply Ohms Law, test kirchhoff’s voltage and current laws in simulated circuit, and fine the condition for max power transfer from source voltage to load. This was accomplished by analyzing simulated circuits with resistors and voltage sources using voltmeters and ammeters to test and verify voltages and currents and use Kirchhoff's rules and Ohm Laws to verify each current, voltage drop and resistance. In part 1 of the lab we used the lead of a pencil and measured the voltage and resistance across the pencil in series. In logger pro we notice that as voltage increases, resistance slowly increases as well, also you need a large increase in Voltage for a decent current increase. Based on the data calculated resistance on the graph is similar to that simulated. 6