Emf V & Potential Difference in a Resistor

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SUMMARY

The discussion focuses on calculating the potential difference across a 0.31 ohm resistor connected to a 2.1 V battery while generating thermal energy at a rate of 11 W. The correct potential difference across the resistor is approximately 1.86 V, derived from the equation P = IV and substituting I with V/R. Additionally, the internal resistance of the battery must be considered to accurately determine the total potential difference, which is not simply the emf of the battery. The confusion arises from not accounting for the internal resistance when calculating the voltage across the resistor.

PREREQUISITES
  • Understanding of Ohm's Law (V = IR)
  • Familiarity with the power equation (P = IV)
  • Basic knowledge of electrical resistance and circuits
  • Concept of internal resistance in batteries
NEXT STEPS
  • Study the relationship between power, voltage, and resistance in electrical circuits
  • Learn about internal resistance in batteries and its impact on circuit performance
  • Explore advanced circuit analysis techniques, including Thevenin's and Norton's theorems
  • Investigate practical applications of resistors in thermal energy generation
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Students studying electrical engineering, physics enthusiasts, and anyone involved in circuit design or analysis who seeks to understand the implications of internal resistance and power calculations in electrical systems.

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Homework Statement



Thermal energy is to be generated in a 0.31 resistor at the rate of 11 W by connecting the resistor to a battery whose emf is 2.1 V.

(a) What potential difference must exist across the resistor?

(b) What must be the internal resistance of the battery?


Homework Equations


P = IV
V = IR


The Attempt at a Solution


I tried manipulating the variables and substituting in the equations. P =IV, 11 = IV, V= IR, 11=I^2*R, 11=I^2*.31, so i divided 11/.31 then took the square root, which was about 6 for the current. I went back and multipled V=IR, to find V=6*.31 , which was 1.86 V. I thought that to find the total potential difference i had to add the emf V given and the V i found from current and resistance, which was 1.86V + the 2.1 V emf... 3.96. But this answer is incorrect.

As for part B, I'm completely lost.
 
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I share your confusion with this question! Only after reading part (b) do we learn that there is a second resistor involved - the internal resistance of the 2.1 Volt battery. So we don't have 2.1 Volts across the 0.31 ohm resistor. So it makes sense to ask what voltage we do have across it, as part (a) does. What do we know about this component? Resistance .31 Ohms, Power 11 Watts. We need a formula that relates V, R and P. One way to derive it is to start with P = IV and replace I with V/R, eliminating the I that we neither know or care to find.
 
Thank you so much, I was definitely over-complicating it in my thinking. Your explanation was really clear. :)
 

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