Posted by sonia on Saturday, November 12, 2011 at 6:07pm.
The magnetic field in the region shown below is increasing by 5 T/s. The circuit shown (with R=25 , C=55 µF, dimensions 1 m by 2 m) is inserted into the region as shown. The capacitor is initially uncharged.
1. How long will it take the capacitor to charge to 25% of its final charge?
Please help I tried T=RC but not right formula!

no picture  Damon, Saturday, November 12, 2011 at 8:09pm
I do not have a picture of your circuit so find this hard to follow. However for an RC circuit at initial voltage V when the switch is closed:
V = i R + (1/C) integral i dt
with i = 0 at t = 0
0 = R di/dt + i/C
0 = RC di/dt + i
let i = Io (e^kt)
di/dt = k Io e^kt
0 = RC kIo e^kt + i
so
i = RC k Io e^kt = Io e^kt
so k = 1/RC
so if in form i = Io e^t/T
T indeed = RC
Now
The voltage around this loop = rate of change of magnetic flux
E = 5*2square meters = 10 volts
so we put a ten volt force on our RC circuit
i = Io e^t/RC
Initially all the voltage appears on the resistor because there is no charge yet on the capacitor
Io = E/R = 10/R
so
i = (10/R)e^t/RC
charge on capacitor Q= integral i dt
= (10 /R) (RC e^t/RC + k)
when t = 0, Q = 0 so
k = RC
so
Q = 10 C (1  e^t/RC)
Q final = 10 C
when does Q = (10/4)C ?
.25 = 1  e^t/RC
e^t/RC = .75
t/RC = ln .75 = .2877
so
t = .2877 R C
Answer This Question
Related Questions
 physics urgent!  The magnetic field in the region shown below is increasing by ...
 physics  A Bainbridge mass spectrometer is shown in the figure. A charged ...
 physics  Answer the following question:Be sure to show all work. Include ...
 Physics  (a) In the LC circuit shown in the figure, the current is in the ...
 Physics  The circuit shown below is in a uniform magnetic field that is into ...
 Physics  Took a leaf out of Eileen's book for the picture corresponding to the ...
 physics  In a region containing a uniform electric field at right angle to the ...
 physics  Two charged particles are projected (in the same plane as the paper) ...
 Physics  A charged particle with mass m, charge q=6.4 ×10−19C and speed...
 Biology  Four different molecules are shown below. For each, indicate if it ...
More Related Questions