Four identical capacitors are connected with a resistor in two different ways. W

Question

Four identical capacitors are connected with a resistor in two different ways. When they are connected as in part a of the drawing, the time constant to charge up this circuit is 0.84 s. What is the time constant when they are connected with the same resistor as in part b?

Four identical capacitors are connected with a resistor in two different ways. When they are connected as in part a of the drawing, the time constant to charge up this circuit is 0.84 s. What is the time constant when they are connected with the same resistor as in part b?

Explanation / Answer

time constant T = Rc

Cnet in figb is    2C and C are in series = 2C

C and C in parallel---> C' = c*c/2C = C/2

C/2 and 2C sre in series,

so Cnet = C/2* 2C/(C/2+2C)

Cnet = 2C/5

from fig T = RC = 0.84

C/2 and C2 in parallel---->CNet = C/2 +C/2 = C

so C = 0.84/R

using this in 2C/5

   Cnet = 2* 0.84/R *5

RCnet = 2*0.84/5    = 0.3636 secs is the time cosntant of part B fig

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