circuits

[Sarahisme]

Hi all,

 

i am having a lot of trouble trying to do this problem, as my textbook does not discuss circuits and it is only covered in 3 very brief lecture slides.

 

 

if anyone would be able to point me to some good websites on how to do these type of problems or be able to help me in any other way that would be great!

 

Thanks guys & gals!

 

-Sarah

[Tartaglia]

Kirchoff's 2nd law gives

 

E(t) = RI(t) + Q(t)/C

 

or E(t)/R = I(t)+ Q(t)/CR

 

differentiating wrt t and setting dQ(t)/dt = I(t) gives

 

(1/R)*dE(t)/dt = dI(t)/dt + I(t)/RC as required

 

(a) dE(t)/dt = 0

 

ie dI(t)/dt + I(t)/RC = 0

 

solving I(t) = I(0)exp(-t/CR) = (Eo/R)*exp(-t/CR)

 

(b) dE(t)/dt = Eo

 

ie dI(t)/dt + I(t)/RC = Eo/R

 

Integrating factor exp(t/CR)

 

I(t)exp(t/CR) = integral (Eo/R)exp(t/CR)

 

 

I(t)exp(t/CR) = EoC*exp(t/CR) + k

 

put I(0) = Eo/R, t = 0

 

k = Eo/R-EoC

 

I(t) = EoC{1-exp(-t/CR)}+ (Eo/R)exp(-t/CR)

 

Please note there looks to be an inconsistent use of units in question which makes the answer look odd. In (a) the unit of Eo is volts whereas in (b) unit of Eo is volts per second

[Sarahisme]

ah ok, i think i see now, thanks for that!