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

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

C_eq = C₁₆ C₂₃₄₅ /(C₁₆ + C₂₃₄₅ )

C_eq = (10) (5.85) /(10 + 5.85)

C_eq = 3.7 uF

b)

Q = charge stored by the combination of capacitors

V = battery Voltage = 27 Volts

Charge stored is given as

Q = C_eq 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