Exponential revision question I can't work out?

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SUMMARY

The discussion revolves around the mathematical problem of transposing the equation i = 12.5(1 - e^(-t/(cr))) to make "t" the subject. The user, Ramjam, initially struggles with the correct steps to isolate "t" using natural logarithms. Key steps include moving the constant 1 to the left side and recognizing that multiplying by -1 can simplify the equation. Ultimately, the correct form is (1 - i/12.5) = e^(-t/(cr)), allowing for further calculations once specific values for current, resistance, and capacitance are substituted.

PREREQUISITES
  • Understanding of algebraic manipulation and transposition of equations.
  • Familiarity with exponential functions and their properties.
  • Knowledge of natural logarithms (ln) and their application in solving equations.
  • Basic concepts of RC circuits, including resistance (R) and capacitance (C).
NEXT STEPS
  • Learn how to isolate variables in exponential equations.
  • Study the properties of natural logarithms and their applications in algebra.
  • Explore RC circuit behavior and calculations involving current, resistance, and capacitance.
  • Practice solving similar equations involving exponential decay and logarithmic functions.
USEFUL FOR

Students in calculus or algebra courses, educators teaching mathematical transposition, and anyone working with exponential equations in physics or engineering contexts.

  • #31
opps sorry that should be -i/12.5-1=e-t/cr
 
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  • #32
Ramjam said:
opps sorry that should be -i/12.5-1=e-t/cr
No, that's not right either. You really need to be more careful.
 
  • #33
in that case i don't under what you mean by
After you multiplied by -1, what happened to the -1?
 
  • #34
What is -1 times i/12.5 - 1?

If you're having such a difficult time with basic algebra, I am very concerned about the prospects of you working with exponential and log equations.
 
  • #35
Mark44 said:
What is -1 times i/12.5 - 1?

If you're having such a difficult time with basic algebra, I am very concerned about the prospects of you working with exponential and log equations.
It was 2am in the uk and after a long working day which i also do along side my course probably wasn't the best idea.

Right here are my working so far now that I've been had some sleep,

we start with I=12.5(1-e-t/cr)

I then divide both sides by 12.5 removing the 12.5 from the right hand side.

I/12.5 = 1-e-t/cr

I then subtract -1 from both sides

I/12.5 -1 = -e-t/cr

I then times both sides by -1 giving me

(1- I/12.5) = e-t/cr

how ever to remove I am unsure of how to go on from here?
 
  • #36
You need the time when the current I reaches the value I=10 A. Note that 12.5 is also in amperes. Substitute 10 for I and evaluate the left side of the equation.
Also calculate cr, or better CR from the given value of capacitance C and resistance R.
 

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