From the second graph read p max and compare with e 2

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From the second graph, read P max and compare with E 2 /4r. Read R for P max and compare with r. Equation 2 states that: Additionally, we know that when P is at a maximum, i 2 r=i 2 R From Table 1 we know that Power is at a maximum when R=50 ohms. Therefore, r=50 ohms. Adapting equation 2: And for comparison, using: Our measured value for P max was .0432 Watts, so to find our percent difference: 3) Show that at maximum power output, the terminal voltage of the battery is half its emf. Proven experimentally- We calculated the emf to be equal to 2.88 Volts in part 2. At maximum power output, the terminal voltage was measured at 1.46 Volts.
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.521 is very close to .5 or, one half the emf, and results in a 4.2% error. Proven theoretically- Q1) Why is a dead battery characterized by a high internal resistance? Higher resistances correlate to lower power outputs. Thus meaning, it stands to reason, that when a battery has no more power to offer (is dead), it must have a very high internal resistance. Q2) Explain why batteries of low current capacity have higher internal resistances than those batteries of high current capacity, e.g. a 12v flashlight battery vs. a 12 v car battery. V=IR, where V is the voltage, I is the current capacity, and R is the resistance. Therefore, I and R are inversely proportional. In order to maintain a constant V, 12 volts for instance, as the current capacity gets lower, the resistance must be much higher to compensate. Conclusion: Overall, this lab was a success. The natural behaviors of batteries were all explained, and the relationships between all the variables involved were demonstrated. Additionally, the numerical results that were derived were relatively accurate, with a percentage error just around 4%. The setup for the lab was somewhat complicated, so improvements might come in the form of more explicit directions or a more simplified setup. Otherwise, the lab was successful overall and demonstrated the accuracy of the equations related to emf.
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