In the figure a 27 V battery is connected across capacitors of capacitances C_1

Question

In the figure a 27 V battery is connected across capacitors of capacitances C_1 = C_6 = 3.5 mu F and C_3 = C_5 = 2.5C_2 = 2.5C_4 = 4.5 mu F. What are (a) the equivalent capacitance C_eq of the capacitors and (b) the charge stored by C_eq? What are (c) V_1 and (d) q_1 of capacitor 1, (e) V_2 and (f) q_2 of capacitor 2, and (g) V_3 and (h) q_3 of capacitor 3? Number ________ Units _______ Number ________ Units _______ Number ________ Units _______ Number ________ Units _______ Number ________ Units _______ Number ________ Units _______ Number ________ Units _______ Number ________ Units _______

Explanation / Answer

a) Ceq = [C4+C2+(C3 series C5)] series [ C1+C6]

       = [4.5+2.5+2.5/2]series [3.5+3.5]

    = 8.25 series 7

   = 8.25*7/[8.25+7]

= 3.787 uF

b) Charge q = Ceq V

    = 3.787*27

= 102.2 uC

d) q1 = q/2 as C1 and C6 have equal capacitance, so equal charge

     = 51.1 uC

c) V1 = q1/C1 = 51.1/3.5

       = 14.6 V

e) v2 = v-v1 = 27-14.6

      = 12.4 V

f) q2 = C2V2 = 12.4*2.5

             = 31 uC

g) V3 = 12.4/2 = 6.2 V

h) q3 = C3V3 = 2.5*6.2 = 15.5 uC

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