A capacitor of capacitance C₁ = 0.1 microfarad withstands the maximum voltage V₁= 6.0 kilovolt. While another capacitor of capacitance C₂ = 2.0 microfarad withstands the maximum voltage V₂ = 4.0 kilovolt. What maximum voltage will the system of these two capacitors withstand if they are connected in series?

Given,
Capacitance on capacitor 1, C₁ = 1.0 μF
Maximum voltage applied across capacitor 1, V₁ = 6 kV = 6 x 10³ V
Capacitance on capacitor 2, C₂ = 2 μF
Maximum voltage applied across capacitor 2, V₂ =4 kV = 4 x 10³ V

Now,
Charge on first capacitor, q₁ = C₁ V₁
                                        = 1.0 x 6 x 10³ μC
                                        = 6000 μC
Charge on second capacitor, q₂ = C₂V₂
                                            = 2.0 x 4 x 10³ μC
                                            = 8000 μC

In series combination, the magnitude of charge on each capacitor must be the same.
As maximum charge on C₁ is 6000 μC, therefore, maximum charge on C₂ must also be 6000 μC.
Hence, maximum voltage for the combination is,

                      $$\begin{gathered} \mathrm{V}\text{'} = \mathrm{V}{\text{'}}_1+\mathrm{V}{\text{'}}_2 \\ = \frac{6000}{1.0}+\frac{6000}{2.0} \\ = 9000 \mathrm{V} \\ = 9 \mathrm{kV} \end{gathered}$$