3.) Use the diagram below to find the following quantities: a) The equivalent ca

Question

3.) Use the diagram below to find the following quantities:
a) The equivalent capacitance.
b) The equivalent charge that would be stored on the equivalent capacitor if the battery voltage (V0) is 9V.
c) The charge stored on each individual capacitor.
d) The voltage across each individual capacitor.
e) The energy stored in each individual capacitor.
3.) Use the diagram below to find the following quantities: a) The equivalent capacitance. b) The equivalent charge that would be stored on the equivalent capacitor if the battery voltage (Vo) is 9v. c) The charge stored on each individual capacitor. d) The voltage across each individual capacitor. e) The energy stored in each individual capacitor. C1 C3 C5 C2 C4

Explanation / Answer

a) C1 and C2 are in series ======> C12 = C1*C2/(C1 + C2) = 1.33 uF

    C3 and C4 are in series ======> C34 = C3*C4/(C3 + C4) = 0.75 uF

    And C12, C34 and C5 are in parallel =====> C = C12 + C34 + C5 = 8.08 uF

b) Equivalent charge = Q = CV = 8.08*10^-6*9 = 72.72 uC

c) and d) Charge in series capacitor remains same and divides in parallel.

      And   Voltage in parallel capacitor remains same and divides in series.

So V5 = 9 V =====> Q5 = C5*V5 = 54 uF

V12 = 5 V ======> Q12 = Q1 = Q2 = C12*V12 = 11.97 uF

V1 = Q1/C1 = 11*97/4 = 3 V

V2 = Q2/C2 = 11.97/2 = 6 V

Similarly, V34 = 5 V ======> Q34 = Q3 = Q4 = C34*V34 = 6.75 uF

V3 = Q3/C3 = 6.75/3 = 2.25 V

V4 = Q4/C4 = 6.75/1 = 6.75 V

e) Energy stored in C1 = U1 = 0.5*C1*V1^2 = 18 uJ

    Energy stored in C2 = U2 = 0.5*C2*V2^2 = 36 uJ

   Energy stored in C3 = U3 = 0.5*C3*V3^2 = 7.6 uJ

   Energy stored in C4 = U4 = 0.5*C4*V4^2 = 22.8 uJ

   Energy stored in C5 = U5 = 0.5*C5*V5^2 = 243 uJ

   

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