Calculus Spreadsheet for an RC circuit

__Calculus__

I have recently been given the following question but I have no idea how to differntiate the equation or plot the equations. Can you please help me?

Capacitor = 100 nF

Resistor = 47 kΩ

Supply voltage = 5 V

Charging characteristic for a series capacitive circuit:

v=V(1- e-^(1/T)) where T=CR

n Use a spreadsheet to plot the charging curve over the range 0 to 20 ms (milliseconds).

n Differentiate the charging equation and find the rate of change of voltage at 6 ms.

re: Calculus Spreadsheet for an RC circuit

Quote:

Originally Posted by

**maali5** __Calculus__

I have recently been given the following question but I have no idea how to differntiate the equation or plot the equations. Can you please help me?

Capacitor = 100 nF

Resistor = 47 kΩ

Supply voltage = 5 V

Charging characteristic for a series capacitive circuit:

v=V(1- e-^(t/T)) where T=CR

n Use a spreadsheet to plot the charging curve over the range 0 to 20 ms (milliseconds).

n Differentiate the charging equation and find the rate of change of voltage at 6 ms.

corrected equation ... voltage across the capacitor is a function of time.

Re: Calculus Spreadsheet for an RC circuit

hint on how to differentiate the equation: V and T are constants. we can re-write the equation as:

v = V - Ve^(-t/T).

the first term in this difference disappears in the derivative, so we only have to take the derivative of -Ve^(-t/T).

the -V in front is just a constant, so v'(t) = (-V)(d/dt)(e^(-t/T))

and e^(-t/T) is of the form e^(at), where in this particular case, a = -1/T.

Re: Calculus Spreadsheet for an RC circuit

Skeeter: Thanks, I made a spelling mistake

Question: Use a spreadsheet to plot the charging curve over the range 0 to 20 ms (milliseconds)

T=CR

T=0,1 x 47000

t=0.00470

Answers:

T v=V(1- e-^(t/T)) How can I draw the spreadsheet when answers =5?

0 v=5(1- e-^(0/T)) 0

1 v=5(1- e-^(1/T)) 5

2 v=5(1- e-^(2/T)) 5

3 v=5(1- e-^(3/T)) 5

4 v=5(1- e-^(4/T)) 5

5 v=5(1- e-^(5/T)) 5

6 Etc,

..

...

...

20 v=5(1- e-^(20/T)) 5

Deveno: Cheers for the hints

Re: Calculus Spreadsheet for an RC circuit

Quote:

Originally Posted by

**maali5** Skeeter: Thanks, I made a spelling mistake

Question: Use a spreadsheet to plot the charging curve over the range 0 to 20 ms (milliseconds)

T=CR

T=0,1 x 47000

t=0.00470

Answers:

T v=V(1- e-^(t/T)) How can I draw the spreadsheet when answers =5?

0 v=5(1- e-^(0/T)) 0

1 v=5(1- e-^(1/T)) 5

2 v=5(1- e-^(2/T)) 5

3 v=5(1- e-^(3/T)) 5

4 v=5(1- e-^(4/T)) 5

5 v=5(1- e-^(5/T)) 5

6 Etc,

..

...

...

20 v=5(1- e-^(20/T)) 5

Deveno: Cheers for the hints

time is in milliseconds, not seconds ...

t should be 0, .001, .002, .003, ... , .020

Re: Calculus Spreadsheet for an RC circuit

Genius! but can you explain how to calculate it.

I know 1 seconds is 1000millisecond.

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Re: Calculus Spreadsheet for an RC circuit

I have done the graph and have the attached to the page.

Is it correct?

Sooory to bother you with questions

Re: Calculus Spreadsheet for an RC circuit

Quote:

Originally Posted by

**maali5** Genius! but can you explain how to calculate it.

I know 1 seconds is 1000millisecond.

sure ...

$\displaystyle V(.001) = 5 \left(1 - e^{-\frac{.001}{.0047}} \right) = 0.95282...$

... and so on. You should do some research on how to do it in a spreadsheet ...

how to generate a graph in excel - Google Search