For the circuit shown below, capacitors A and B have identical geometry, but a material of dielectric constant 3 is present between the plates of B. The potential difference across A and B are respectively

Options

A. `2.5 V, 7.5 V`
B. `2 V, 8 V`
C. `7.5 V, 2.5 V`
D. `8 V, 2 V`

Answer

A

Explanation

If `C_(0) =` capacitance with air between plates. Then, `3C_(0) =` capacitance with dielectric. As capacitors each in series, equivalent capacitance is given by
`(1)/(C_(eq)) = (1)/(C_(0)) + (1)/(3C_(0)) rArr C_(eq) = (3)/(4)C_(0)`
Now, `C_(eq) = (Q)/(V) rArr Q = 10xx(3)/(4)C_(0)`
Also, charge on each capacitor is same. Charge on each capacitor is `(15)/(2)C_(0) = Q`
`:.` Potential drop across capacitors is
`V_(A) = (Q)/(C_(A)) = ((15)/(2).C_(0))/(C_(0)) = (15)/(2) = 7.5 V`
`V_(B) = (Q)/(C_(B)) = ((15)/(2)C_(0))/(3C_(0)) = (5)/(2) = 2.5 V`