Two condensers `A` and `B` each having slabs of dielectric constant `K = 2` are connected in series. When they are connected across `230 V` supply, potential difference across `A` is `130 V` and that across B is `100 V`. If the dielectric in the condenser of smaller capacitance is replaced by one for which `K = 5`, what will be the values of potential difference across them?

Explanation

In series, potential differece distributes in inverse ratio of capacitance
`:. V_A/V_B=C_2/C_1` or `130/100=C_2/C_1`
or `C_1=C_2/1.3=C_A`
`k` is made `2.5` times. Therefore `C_1` will also become `2.5` times.
`C_1^'=2.5C_1=(2.5C_2)/1.3`
or `C_1^'=25/13`
now, `V_A^'/V_B^'=C_2/C_1=13/25` ltbgt or `V_A^'=(13/(13+25))(230)=78.68V`
`V_B^'230-V_B^'=151.32V`