Math Problem Statement

N=1/(2piRC) search C

Solution

ToTo solve solve for for \( C C \) in in the the equation equation ( ( N N = = \ \fracfrac{{11}{}{22\ \pipi RC R} C }), \ follow), these we steps isolate:

(### C Given : ).\ Here's[ theN step =-by -stepfrac process{:

11.}{2 Start with\pi the RC given} equation: ]

### Rear[ range for N = C \frac: {11.}{2 Multiply both \ sidespi by R C ( } 2 \ \pi]

RC2 .) Multiply to both eliminate sides by the ( denominator: 2 \ \pi[ R N C \ )cdot to eliminate2 the\ denominatorpi: RC = \ [ 1 N \ \cd]

ot2 .2 Divide \pi both sides R by C ( = 12 \ pi R \ ]

)3 to. isolate Divide ( both C sides \ by (): \2 pi R C = N \ \frac){ to1 isolate}{ \( C2\ \pi): RN } \ [

C### = Final \ Expressionfrac{ for1 }{ C2 \: pi[ R NC =} \frac {]

1###}{ Final2 Answer: pi\ RN[ } C\ =]

\Letfrac me{ know1 if}{ you2 would \pi like numerical R calculations N or} \ further]

clarificationsWould.

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like** furtherQuestions for clarification or examples you to using explore specific: values** for1 . R \ How) is the and constant \( N \(?2\

pi### \ Related) Questions derived: in1 this. equation What, does the and why constant is ( \ it relevantpi? \2). represent What, are and the why is typical units it of used inRthisequationin R this equation,? 2 .CHow. C How, does and changing \( N R \? )3 affect. the How value does of \( C C \)? change3 as. ( Can this N \ equation) be increases applied in or decreases electrical? circuits4 (.e Can.g you., solve RC a circuits similar)? equation4 for. How R would \ the) unit or of \( \( N C \) instead be? derived5 based. on What this formula real-world? systems5 use. this If type ( of N formula = ( e50 .g.,) electrical Hz circuits and)?

(** RTip =:** When100 solving \ for) a Oh variablems,, carefully what handle is constants the and value units of to ( avoid C errors !)?

Tip:

Always ensure units are consistent when plugging in values, especially in physics-related equations involving time, resistance, and capacitance.

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Math Problem Analysis

Mathematical Concepts

Algebra
Rearranging Equations
Capacitance

Formulas

N = 1/(2πRC)
C = 1/(2πRN)

Theorems

Basic algebraic manipulation

Suitable Grade Level

Grades 10-12