DC circuits (emf, battery power, resistance)

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SUMMARY

The discussion centers on the impossibility of a scenario involving a battery with an emf of 9.2V and an internal resistance of 1.2 ohms, supplying a power of 21.2W to an external resistor. The equations provided, including ΔV = ε - Ir and P = IΔV, are crucial for analyzing the circuit. The key takeaway is that the current must be calculated to determine the feasibility of the power extraction, which is not achievable under the given conditions. The relationship between internal resistance and power dissipation is essential for understanding the limitations of this circuit.

PREREQUISITES
  • Understanding of Ohm's Law and circuit analysis
  • Familiarity with power equations in electrical circuits
  • Knowledge of internal resistance in batteries
  • Ability to manipulate algebraic equations for circuit calculations
NEXT STEPS
  • Learn how to calculate current using I = ε/(R+r)
  • Explore the concept of maximum power transfer theorem
  • Study the effects of internal resistance on battery performance
  • Investigate power dissipation in resistive circuits using P = I²R
USEFUL FOR

This discussion is beneficial for electrical engineering students, circuit designers, and anyone interested in understanding the limitations of battery-powered circuits and power dissipation principles.

travh2007
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Homework Statement



Why is the following situation impossible? A battery has an emf of E = 9.2V and an internal resistance of r = 1.2 ohms. A resistance R is connected across the battery and extracts from it a power of P = 21.2W.

Homework Equations



My book gives these equations throughout the section:
\DeltaV = \epsilon - Ir

\epsilon = IR + Ir

I = \epsilon/(R+r)

P=I\DeltaV

The Attempt at a Solution



I tried plugging in some of my values into some of these formulas, but I don't know the current, so therefore any formula with I in it, I couldn't do. Can someone steer me in the correct direction somehow please?
 
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Presumably they mean that the external resistor is to dissipate 21.2W .

Here are some additional relationships for power that you might find useful in your career:

P = I*V = I2R = V2/R

You should be able to write an expression for the power dissipated in the external resistor given its value, and determine the conditions for maximum possible dissipation.
 

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