Three capacitors having capacitances of 81 muF 81 muF and 50

Three capacitors having capacitances of 8.1 muF, 8.1 muF. and 5.0 muF are connected in series across a 30-V potential difference. What is the charge on the 5.0 muF capacitor? Express your answer using two significant figures. Q_3 =_________What is the total energy stored in all three capacitors? Express your answer using two significant figures. U =_____Part C The capacitors are disconnected from the potential difference without allowing them to discharge. They are then reconnected in parallel with each other, with the positively charged plates connected together. What is the voltage across each capacitor in the parallel combination? Express your answer using two significant figures. V =________Part D What is the total energy now stored in the capacitors? Express your answer using two significant figures. U =__________

Solution

A. all three capacitors are connected in series hence charge on
each capacitor will be same.

equivalent capacitance of all three will be Ceq then

for series connection,

1/Ceq = 1/C1 + 1/C2 + 1/C3 = 1/8.1 + 1/8.1 + 1/5

Ceq = 2.24 uF

Q = Ceq V = 2.24 uF x 30 V = 67.13 uC Or 67.13 x 10^-6 C

B) total energy stored.

= Ceq V^2 /2

= (2.24 x 10^-6) ( 30^2) /2 = 1.008 x 10^-3 J

C) suppose voltage across each capacitor is V and charge on each is
Q1, Q2 and Q3.

using charge conservation,

Q1 + Q2 + Q3 = 3Q

and Q1 = C1V, Q2 = C2V , Q3 = C3V

V(C1 + C2 +C3) = 3Q

V( 8.1 + 8.1 + 5) uF = 3 ( 67.13)

V = 9.5 Volt ........Ans

D. now total energy = V^2 ( C1 + C2 + C3)^2 /2

= 9.5^2 ( 8.1 + 8.1 + 5) x 10^-6 / 2

= 9.57 x 10^-4 J