Consider the following figure. (i) (a) Find the equivalent capacitance between [Free] B119
Consider the following figure. (i) (a) Find the equivalent capacitance between points a and b for the group of capacitors connected as shown in the figure if C1=4.00μF,C2=14.00μF, and C3=2.00μF. Your response differs from the correct answer by more than 10%. Double check your calculations. μF (b) If the potential between points a and b is 60.0 V , what charge is stored on C3 ? minimize roundoff error. μC
![Consider the following figure. (i) (a) Find the equivalent capacitance between [Free] B119](data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%201024%20325'%3E%3C/svg%3E)
Answer
Capacitor Network: Equivalent Capacitance and Charge Calculation
🔷 Given Values
- C₁ = 4.00 μF
- C₂ = 14.00 μF
- C₃ = 2.00 μF
🔹 Step (a): Equivalent Capacitance
👉 Between point b and c:
Ccb = C₂ + C₂ = 2 × 14 = 28 μF
👉 Capacitors C₁ and C₂ in series between a and c:
C12 = (C₁ × C₂) / (C₁ + C₂) = (4 × 14) / (4 + 14) = 56 / 18 = 3.11 μF
👉 Total capacitance between a and c (2 × C12 in parallel with C₃):
Cac = 2 × 3.11 + 2 = 8.22 μF
👉 Ccb and Cac in series:
Ceff = (Ccb × Cac) / (Ccb + Cac) = (28 × 8.22) / (28 + 8.22) = 230.16 / 36.22 = 6.35 μF
🔹 Step (b): Charge and Voltage Calculation
👉 Potential difference across a and b is 60 V.
👉 Total charge:
Q = C × V = 6.35 × 60 = 381 μC
👉 Voltage across a and c:
Vac = Q / Cac = 381 / 8.22 = 46.35 V
👉 Charge on capacitor C₃:
Q₃ = C₃ × Vac = 2 × 46.35 = 92.7 μC
✅ Final Answers:
- Equivalent Capacitance (Ceff) = 6.35 μF
- Charge on C₃ (Q₃) = 92.7 μC