A circuit consisting of 4 capacitors: C1=6 ?F, C2=2 ?F, C3=4 ?F, C4=3 ?F is conn

Question

A circuit consisting of 4 capacitors: C1=6 ?F, C2=2 ?F, C3=4 ?F, C4=3 ?F is connected to the 6 V battery.
a) Find the equivalent capacitance of the circuit Ceq .
b) Find the charge on capacitor 1.
c) Find voltage on capacitor 2.
d) Find energy stored in capacitor 3.

A circuit consisting of 4 capacitors. C1-6 ur, C2-2 , C3-4 F, C,-3 UF is connected to the 6 V battery a) Find the equivalent capacitance of the circuit Ceq b) Find the charge on capacitor C2 4 c) Find voltage on capacitor 2 d) Find energy stored in capacitor 3.

Explanation / Answer

a) C2 and C3 are in parallel then, their equivalen C23 is

C23 = C2 + C3 = 2 F + 4 F = 6 F

now, capacitors C23 and C1 are in series then, their equivalent C123 is

C123 = ( C1 * C23 ) / ( C1 + C23 ) = ( 6 F * 6 F ) / ( 6 F + 6 F ) = 3 F

finally, capacitors C123 and C4 are in parallel then, their equivalent is the equivalent capacitance of the circuit

Ceq = C123 + C4 = 3 F + 3 F = 6 F

b) the charge stored by C123 is the charge stored by C1

Q123 = C123 = ( 3 F ) ( 6 v ) = 18 C

then

Q1 = Q23 =Q123 = 18 C

c) the voltage on capacitor C23 is the voltage on capacitor C2 , then

V23 = Q23 / C23 = ( 18 C ) / ( 6 F ) = 3 v

then

V2 = V3 = V23 = 3 v

d) the energy stored by the capacitor C3 is U3 = ( C3 V3^{2} ) / 2

U3 = ( 4 F * ( 3 v )^{2} ) / 2 = 18 J

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