Question

In the figure a 27 V battery is connected across capacitors of capacitances C1-C6 5.0 μF and C3-C5-2.5C2-2.5C4-4.5 what are (a) the equivalent capacitance Ceq of the capacitors and (b) the charge stored by Ceq? What are (c) V and (d) q1 of capacitor 1, (e) V2 and (f) q2 of capacitor 2, and (g) V3 and (h) 43 of capacitor 3? G C Ci Gi (a) Number (b) Number 122.04 (c) Number 12.20 (d) Number 55.144 (e) Number (f) Number 4.52 Units F UnitsHC Units v UnitsC Units Units

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Answer #1

a)

C3 and C5 are in series and their combination is given as

C35 = C3 C5/(C3 + C5) = (4.5) (4.5)/(4.5 + 4.5) = 2.25 uF

C2 , C4 and C35 are in parallel and their combination is given as

C2345 = C2 + C4 + C35 = 1.8 + 1.8 + 2.25 = 5.85 uF

C1 and C6 are in parallel and their combination is given as

C16 = C1 + C6 = 5 + 5 = 10 uF

C16 and C2345 are in series and their combination is given as

Ceq = C16 C2345 /(C16 + C2345 )

Ceq = (10) (5.85) /(10 + 5.85)

Ceq = 3.7 uF

b)

Q = charge stored by the combination of capacitors

V = battery Voltage = 27 Volts

Charge stored is given as

Q = Ceq V

Q = (3.7) (27)

Q = 99.9 uC

c)

V1 = Voltage across C1 = V16 = Voltage across the combination of C1 and C6 (Since in parallel voltage remain the same)

Q1 = charge in C1 = Q16 = charge in C16 = Q = 99.9 uC                  (Since charge remain same in series)

Using the equation

Q1 = C1 V1

99.99 = (5) V1

V1 = 19.98 Volts

d)

Q1 = charge in C1 = Q16 = charge in C16 = Q = 99.9 uC  

e)

V2 = Voltage across C2 = Voltage across the parallel combination C2345 = V - V16 = 27 - 19.98 = 7.02 Volts   (Since in parallel voltage remain the same)

f)

Q2 = charge in C2 = ?

Using the equation

Q2 = C2 V2

Q2 =(1.8) (7.02)

Q2 = 12.6 uC

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