A) 5
B) 1.25
C) 4
D) 2.5
Correct Answer: A
Solution :
In air the potential difference between the plates \[{{V}_{air}}=\frac{\sigma }{{{\varepsilon }_{0}}}\cdot d\] ... (i) In the presence of partially filled medium potential difference between the plates \[{{V}_{m}}=\frac{\sigma }{{{\varepsilon }_{0}}}\left( d-t+\frac{t}{K} \right)\] ? (ii) Potential difference between the plates with dielectric medium and increased distance is \[{{V}_{m}}=\frac{\sigma }{{{\varepsilon }_{0}}}\left\{ (d+d)-t+\frac{t}{k} \right\}\] ... (iii) According to question\[{{V}_{air}}={{V}_{m}}\]which gives \[K=\frac{t}{t-d}\] Hence, \[K=\frac{2}{2-1.6}=5\]
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