Five capacitors of capacitances C₁ = C₂ = C₃ = C₄ = 10 F and C₅ = 2.5 F are connected as shown, along with a battery of 50 V. The equivalent capacitance and the charges on each capacitor respectively are :

Step-by-step solution

From the given circuit diagram, the capacitors C₁, C₂, C₃ , and C₄ are connected in series. This series combination is connected in parallel with the capacitor C₅ . The entire combination is connected across the 50 V battery. Let C_s be the equivalent capacitance of the series branch containing C₁, C₂, C₃ , and C₄ . 1 C_s = 1 C₁ + 1 C₂ + 1 C₃ + 1 C₄ 1 C_s = 1 10 + 1 10 + 1 10 + 1 10 = 4 10 F ⁻¹ C_s = 2.5 F The total equivalent capacitance C_ eq of the circuit is the sum of the parallel capacitances C_s and C₅ : C_