DC Transients cap+resistor in series Theory

Hi Everyone,

I have a theory explination for a cap and resitor in series but the explination dissapears at the point on the photo.

i understand the theory of all the voltages must add to make the supply

could someone go through it starting with i=dq/dt im happy to answer any questions as i might know more than i remember



Cheers

Corky said:

Hi Everyone,

I have a theory explination for a cap and resitor in series but the explination dissapears at the point on the photo.

i understand the theory of all the voltages must add to make the supply

could someone go through it starting with i=dq/dt im happy to answer any questions as i might know more than i remember

View attachment 90142

Cheers

Click to expand...

What is the question? As far as is shown, it looks like standard algebraic substitution. Where or what don't you understand?

Ratch

the line you just cant read says;
"integrating both sides of the above equation"

rumpfy said:

the line you just cant read says;
"integrating both sides of the above equation"

Click to expand...

Yes, that will solve the differential equation because the variables are separated. And the question is?

Ratch

Hi all,

im ok with algebra but im unsure what the letters represent as they dont state in the question.

does: dq=a given point of charge
dt= a given point in time
Q=CVc = charge is equal to capacitor value x voltage across the cap

if this is right i think ive got my head around it. its just a simple thing but im trying to get my head around what each letter represents

Cheers guys, P.S. sorry for the late reply

Electric current is defined as; the rate of flow of charge. So, within an interval of time, if an amount of charge flows, then the current is (amount of charge /time interval). So mathematically, current i = q/t
For time varying circuit analysis, the time period is mathematically reduced to 'zero' and the incremental current is described as dq/dt and this means the (incremental change of charge/ a small increment of time). Summing the change of charge over time (integration) gives the total charge and hence the capacitor voltage from Vc= Qtot/C as you have said.

does: dq=a given point of charge
dt= a given point in time

Click to expand...

Not really.

I am thinking that you have never studied calculus, defferentiation and integration.

dv/dt is the rate of change of voltage with time, and similarly
dq/dt is the rate of change of charge with time.

The letter d can be thought of as representing "a very small change in".

JimB

Hi,

I am terrible at explaining what im thinking, i knew that but i didnt realise d was "a small change in" i thaught it was a sample of a changing number and not a range

Cheers

yes. d is called or spoken as: "diddly"

Hi,

Often the lower case 'd' is taken to be "delta" which is used to indicate a small change in the variable that follows. So a few examples:
dt: a small change in t
dq: a small change in q
dv: a small change in v
di: a small change in i

and usually we'll see them in pairs being divided by another like:
dv/dt
which means "the change in voltage with respect to time", or more literally, "a small change in voltage as the time changes by a small amount".

When you integrate one of these by the respective variable you get the top variable as result, plus an as yet undefined constant:
Integral(dv/dt) with respect to time = v+K
Integral(di/dt) with respect to time = i+K