The effective capacitance of the parallel combination of two capacitors C₁ and C₂ is 10 μ F. When these capacitors are individually connected to a voltage source of 1 V, the energy stored in the capacitor C₂ is 4 times that in C₁. If these capacitors are connected in series, their effective capacit…

Question

The effective capacitance of the parallel combination of two capacitors C₁ and C₂ is 10 μ F. When these capacitors are individually connected to a voltage source of 1 V, the energy stored in the capacitor C₂ is 4 times that in C₁. If these capacitors are connected in series, their effective capacitance will be

Accepted Answer

(1) 1.6 μ F. At the same voltage U=1/2CV², so the energies are in the ratio of the capacitances: C₂=4C₁. With C₁+C₂=10 μ F, 5C₁=10, so C₁=2 μ F and C₂=8 μ F. In series, Cₛ=(C₁C₂)/(C₁+C₂)=(2×8)/(10)=1.6 μ F.

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