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Two capacitances of capacity $C_1$ and $C_2$ are connected in series and potential difference $V$ is applied across it. Then the potential difference across ${ }^{C_1}$ will be
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$V \frac{C_2}{C_1+C_2}$
Charge flowing $=\frac{C_1 C_2}{C_1+C_2} v$. So potential difference across $C_1=\frac{C_1 C_2 V}{C_1+C_2} \times \frac{1}{C_1}=\frac{C_2 V}{C_1+C_2}$
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