A) 5
B) 1.25
C) 4
D) 2.5
Correct Answer: A
Solution :
In air the potential difference between the plates \[{{V}_{air}}=\frac{\sigma }{{{\varepsilon }_{0}}}.d\] ..... (i) In the presence of partially filled medium potential difference between the plates \[{{V}_{m}}=\frac{\sigma }{{{\varepsilon }_{0}}}(d-t+\frac{t}{K})\] ..... (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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