First slide

Insertion of dielectric in capacitor

Question

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 space there is another plate of thickness $t_{2}$ and dielectric constant $k_{2}$ . The potential difference across the condenser will be

Easy

A

$\frac{Q}{A ε_{0}} (\frac{t_{1}}{k_{1}} + \frac{t_{2}}{k_{2}})$
B

$\frac{ε_{0} Q}{A} (\frac{t_{1}}{k_{1}} + \frac{t_{2}}{k_{2}})$
C

$\frac{Q}{A ε_{0}} (\frac{k_{1}}{t_{1}} + \frac{k_{2}}{t_{2}})$
D

$\frac{ε_{0} Q}{A} (k_{1} t_{1} + k_{2} t_{2})$

Solution

Potential difference across the condenser
$V = V_{1} + V_{2} = E_{1} t_{1} + E_{2} t_{2} = \frac{σ}{K_{1} ε_{0}} t_{1} + \frac{σ}{K_{2} ε_{0}} t_{2} \Rightarrow V = \frac{σ}{ε_{0}} (\frac{t_{1}}{K_{1}} + \frac{t_{2}}{K_{2}}) = \frac{Q}{A ε_{0}} (\frac{t_{1}}{K_{1}} + \frac{t_{2}}{K_{2}})$

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