| A parallel plate capacitor is of area \[6\,\,C{{m}^{2}}\] and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants \[{{K}_{1}}=10,\] \[{{K}_{2}}=12\] and \[{{K}_{3}}=14.\]The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be: |
 |
A) 4
B) 14
C) 12
D) 36
Correct Answer: C
Solution :
| \[{{C}_{net}}={{C}_{1}}+{{C}_{2}}+{{C}_{3}}\] |
| \[\frac{kA{{E}_{o}}}{d}={{k}_{1}}\left( \frac{A}{3} \right)\frac{{{E}_{o}}}{d}+{{k}_{2}}\left( \frac{A}{3} \right)\frac{{{E}_{o}}}{d}+{{k}_{3}}\left( \frac{A}{3} \right)\frac{{{E}_{o}}}{d}\] |
| \[k=\frac{{{k}_{1}}+{{k}_{2}}+{{k}_{3}}}{3}=12.\] |
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