Between the plates of a parallel plate condenser, a plate of thickness `t_(1)` and dielectric constant `k_(1)` is placed. In the rest of the space, there is another plate of thickness `t_(2)` and dielectric constant `k_(2)`. The potential difference across the condenser will be

Options

A. `(Q)/(A epsilon_(0))((t_(1))/(k_(1))+(t_(2))/(k_(2)))`
B. `(epsilon_(0)Q)/(A)((t_(1))/(k_(1))+(t_(2))/(k_(2)))`
C. `(Q)/(A epsilon_(0))((k_(1))/(t_(1))+(k_(2))/(t_(2)))`
D. `(epsilon_(0)Q)/(A) (k_(1)t_(1) + k_(2)t_(2))`

Answer

A

Explanation

Potential difference across the condenser
`V = V_(1) + V_(2) = E_(1)t_(1) + E_(2)t_(2) = (sigma)/(K_(1)epsilon_(0)) + (sigma)/(K_(2)epsilon_(0)) t_(2)`
`rArr V = (sigma)/(epsilon_(0)) ((t_(1))/(K_(1))+(t_(2))/(K_(2))) = (Q)/(A epsilon_(0)) ((t_(1))/(K_(1))+(t_(2))/(K_(2)))`