An uncharged capacitor and a resistors are connected in series to a battery (whe

Question

An uncharged capacitor and a resistors are connected in series to a battery (where C = 24V, C = 4 mu F, and R = 8 times 10^5 Ohm. When the switch is on, the charging begins. Calculate the time constant of the circuit Calculate the maximum charge on the capacitors. Calculate the maximum current in the circuit. Calculate the charge and current as function of time. About how many time constants is the charge on the capacitor 63% its maximum charge value? Two spherical conductors of radius r_1 = 1m, and r_2 = 2m are connected by a conductor wire. The distance of the two conductor spherical conductors are large so that their interaction are negligible. Now 12 mu C charge is placed on the spherical conductors. After the charge on the sphere are in equilibrium. Write down two equations and calculate the electric potential and electric charge on both spheres.

Explanation / Answer

7)given v=24volts

c=4x10^-6F

R=8*10^5ohms

a)time constant =RC

=8*10^5x4x10^-6seconds

=3.2 seconds

b)maximum chagre stored on the capacitor is

q=cv

=4x10^-6Fx24v

=96x10^-6coulomb

c)maximum current in the circuit

i=v/R

=24/(8X10^5))=3X10^-5A

d)the charge and current as a function of time is

q=Q(1-e^-(t/cR)) here Q=cv

current

i=dq/dt

i=i0e^(-t/cR) here i0=v/R

e)given q=63%of maximum charge

0.63Q=Q(1-e^-(t/cR))

e^-t/CR)=1-0.63

=0.37

t/cR=-log(0.37)

t=cR(0.43)

after 0.43 time constants the charge on the charge on the capacitor is 63%of maximum charge

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