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2. Electric potential and capacitance — Physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 SciencePhysics2. Electric potential and capacitance1 Mark
MCQ
A combination of parallel plate capacitors is maintained at a certain potential difference When a $3\, mm$ thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by $2.4\, mm$. Find the dielectric constant of the slab. 
  • A
    $3$
  • B
    $4$
  • ✓
    $5$
  • D
    $6$
✓

Answer

Correct option: C.
$5$
c
Before introducing a slab capacitance of plates

$C_{1}=\frac{\varepsilon_{0} A}{3}$

If a slab of dielectric constant $K$ is introduced between plates then

$C=\frac{K \varepsilon_{0} A}{d}$ then $C'_1 = \frac{{{\varepsilon _0}A}}{{2.4}}$

$\mathrm{C}_{1}$ and ${C'}_{1}$ are in series hence,

$\frac{{{\varepsilon _0}A}}{3} = \frac{{{\text{k}}\frac{{{\varepsilon _0}A}}{3} \cdot \frac{{{\varepsilon _0}A}}{{2.4}}}}{{{\text{k}}\frac{{{\varepsilon _0}A}}{3} + \frac{{{\varepsilon _0}{\text{A}}}}{{2.4}}}}$

$3\, k=2.4 \,k+3$

$0.6\, \mathrm{k}=3$

Hence, the dielectric constant of slap is given by,

$k=\frac{30}{6}=5$

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