JEE PYQ: Capacitance Question 6
Question 6 - 2021 (18 Mar Shift 1)
A parallel plate capacitor has plate area 100 m$^2$ and plate separation of 10 m. The space between the plates is filled up to a thickness 5 m with a material of dielectric constant of 10. The resultant capacitance of the system is ‘x’ pF. The value of $\epsilon_0 = 8.85 \times 10^{-12}$ F$\cdot$m$^{-1}$
The value of ‘x’ to the nearest integer is ____
Show Answer
Answer: 161
Solution
$A = 100$ m$^2$. $C_1 = \frac{k\epsilon_0(100)}{5} = 200\epsilon_0$. $C_2 = \frac{\epsilon_0(100)}{5} = 20\epsilon_0$. $C_1$ & $C_2$ are in series so $C_{eqv} = \frac{C_1 C_2}{C_1 + C_2} = \frac{4000\epsilon_0}{220} = 160.9 \times 10^{-12} \simeq 161$ pF.
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