Ideal Batteries' Internal Resistance

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SUMMARY

The discussion centers on calculating the internal resistance (r) of a real battery modeled as an ideal emf of 12 V in series with its internal resistance. Given the external resistances R1 = R3 = 59 Ω, R4 = R5 = 79 Ω, and R2 = 140 Ω, the measured terminal voltage is 11.61 V. The relationship between the battery voltage (Vb), the ideal voltage (Vo), and the resistances is established through the equation Vb = Vo((R/r)/(1+R/r)). This equation is essential for determining the internal resistance of the battery.

PREREQUISITES
  • Understanding of Ohm's Law and circuit analysis
  • Familiarity with series and parallel resistor combinations
  • Knowledge of voltage dividers and their applications
  • Basic proficiency in solving algebraic equations
NEXT STEPS
  • Research the concept of internal resistance in batteries and its impact on performance
  • Learn about voltage dividers and their practical applications in circuit design
  • Explore advanced circuit analysis techniques, including Thevenin's and Norton's theorems
  • Study the effects of varying load conditions on battery voltage and internal resistance
USEFUL FOR

Electrical engineering students, circuit designers, and anyone interested in understanding battery performance and internal resistance calculations.

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Homework Statement


A circuit is constructed with five resistors and one real battery as shown above right. We model. The real battery as an ideal emf V = 12 V in series with an internal resistance r as shown above left. The values for the resistors are: R1 = R3 = 59 Ω, R4 = R5 = 79 Ω and R2 = 140 Ω. The measured voltage across the terminals of the batery is Vbattery = 11.61 V.
What is r, the internal resistance of the battery?

Homework Equations


Vb = Vo((R/r)/(1+R/r))
Vb= voltage across battery terminals
Vo= Internal voltage
r= internal resistance
R= external resistance
Total ext. resistance in parallel: 1/Rt= 1/r1 + 1/r2
total ext. resistance in series: Rt = r1 + r2

The Attempt at a Solution


Taking total resistance dividing by the amperage.
 
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No figure attached.
 
Taking total resistance dividing by the amperage.

That would just give you the ideal voltage which is already known.

Hint: Potential divider
 

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