A capacitor is charged to a potential of 12.0 V and isthen connected to a voltmeter having an internalresistance of 3.80 MS. After a time of 3.00 s, thevoltmeter reads 3.0 V.Part AWhat is the capacitance of the circuit?Express your answer with the appropriate units.C =SubmitPart BT =ValueRequest AnswerSubmitWhat is the time constant of the circuit?Express your answer with the appropriate units.ValueUnitsRequest AnswerPOUnits??

Answered: A capacitor is charged to a potential…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

A capacitor is charged to a potential of 12.0 V and is
then connected to a voltmeter having an internal
resistance of 3.80 MS. After a time of 3.00 s, the
voltmeter reads 3.0 V.
Part A
What is the capacitance of the circuit?
Express your answer with the appropriate units.
C =
Submit
Part B
T =
Value
Request Answer
Submit
What is the time constant of the circuit?
Express your answer with the appropriate units.
Value
Units
Request Answer
PO
Units
?
?

Expert Solution

Step 1: Capacitance and voltage

Write the expression for the voltage and substitute the corresponding values to calculate the capacitance of the circuit.

$table row cell V equals V subscript 0 e to the power of negative fraction numerator t over denominator R C end fraction end exponent end cell row cell 3.0 text V end text equals left parenthesis 12.0 text V end text right parenthesis e to the power of negative fraction numerator 3.00 text s end text over denominator left parenthesis 3.80 text M end text capital omega cross times fraction numerator 10 to the power of 6 text end text capital omega over denominator 1 text M end text capital omega end fraction right parenthesis C end fraction end exponent end cell row cell fraction numerator 3.0 text V end text over denominator 12.0 text V end text end fraction equals e to the power of negative fraction numerator 3.00 text s end text over denominator left parenthesis 3.80 text M end text capital omega cross times fraction numerator 10 to the power of 6 text end text capital omega over denominator 1 text M end text capital omega end fraction right parenthesis C end fraction end exponent end cell row cell 0.25 equals e to the power of negative fraction numerator 3.00 text s end text over denominator left parenthesis 3.80 text M end text capital omega cross times fraction numerator 10 to the power of 6 text end text capital omega over denominator 1 text M end text capital omega end fraction right parenthesis C end fraction end exponent end cell row cell ln left parenthesis 0.25 right parenthesis equals negative fraction numerator 3.00 text s end text over denominator left parenthesis 3.80 text M end text capital omega cross times fraction numerator 10 to the power of 6 text end text capital omega over denominator 1 text M end text capital omega end fraction right parenthesis C end fraction ln left parenthesis e right parenthesis end cell end table$

Further,

$table row cell negative 1.386 equals negative fraction numerator 3.00 text s end text over denominator left parenthesis 3.80 text M end text capital omega cross times fraction numerator 10 to the power of 6 text end text capital omega over denominator 1 text M end text capital omega end fraction right parenthesis C end fraction cross times 1 end cell row cell C equals fraction numerator 3.00 text s end text over denominator left parenthesis 3.80 text M end text capital omega cross times fraction numerator 10 to the power of 6 text end text capital omega over denominator 1 text M end text capital omega end fraction right parenthesis left parenthesis 1.386 right parenthesis end fraction end cell row cell C equals 5.696 cross times 10 to the power of negative 7 end exponent text F end text end cell row cell C almost equal to 5.7 cross times 10 to the power of negative 7 end exponent text F end text end cell end table$

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