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
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Potential difference across the condenser
$V = V_1 + V_2 = E_1 t_1 + E_2 t_2 = \frac{\sigma}{K_1 \varepsilon_0} t_1 + \frac{\sigma}{K_2 \varepsilon_0} t_2$
⇒ ⇒ $V = \frac{\sigma}{\varepsilon_0} \left( \frac{t_1}{K_1} + \frac{t_2}{K_2} \right) = \frac{Q}{A \varepsilon_0} \left( \frac{t_1}{K_1} + \frac{t_2}{K_2} \right)$
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