Two capacitors of capacitance 2 μF and 4 μF respectively are connected in series. The combination is connected across a potential difference of 10 V. The ratio of the energies stored by the capacitors will be .

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(1) 2:1. Given: C₁=2 μF and C₂=4 μF in series across 10 V. Idea: in series both capacitors carry the same charge Q, so use U=(Q²)/(2C). With Q common, U∝1/C, and (U₁)/(U₂)=(C₂)/(C₁)=4/2=2. Check with numbers: Cₛ=(2×4)/(2+4)=4/3 μF and Q=(40)/3 μC, so V₁=(20)/3 V and V₂=(10)/3 V. So U₁:U₂=2:1 — the smaller capacitor takes the larger share of the voltage and stores more energy.

Two capacitors of capacitance 2 μF and 4 μF respectively are connected in series. The combination is connected across a potential difference of 10 V. The ratio of the energies stored by the capacitors will be ______.

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