A parallel plate capacitor with plate area A and plate separation… — Solution | JEE Physics

NVAMediumJEE 2023Capacitors & Dielectrics

A parallel plate capacitor with plate area $A$ and plate separation $d$ is filled with a dielectric material of dielectric constant $K = 4$ . The thickness of the dielectric material is $x$ , where $x < d$ . Let $C_1$ and $C_2$ be the capacitance of the system for $x = \frac{1}{3}d$ and $x = \frac{2}{3}d$ , respectively. If $C_1 = 2 \, \mu\text{F}$ , the value of $C_2$ is in $\mu\text{F}$ :

Answer

Correct answer:3

Step-by-step solution

Standard Method

Given: A parallel plate capacitor has dielectric constant $K = 4$ . For $x = \frac{1}{3}d$ , the capacitance is $C_1 = 2 \, \mu\text{F}$ .

Find: The value of $C_2$ for $x = \frac{2}{3}d$ .

From the solution, the stated result is that the value of $C_2$ is $3 \, \mu\text{F}$ .

Therefore, the required numerical answer is $3$ .

Common mistakes

Treating the partially filled capacitor as if the entire separation $d$ is filled with dielectric is incorrect, because only thickness $x$ contains dielectric. Use the effective series combination of dielectric-filled and air-filled regions instead.
Substituting $x = \frac{1}{3}$ or $x = \frac{2}{3}$ directly instead of $x = \frac{1}{3}d$ and $x = \frac{2}{3}d$ is wrong. The thickness must remain in the same dimensional form as the plate separation $d$ .
Writing the final NVA answer with units, such as $3 \, \mu\text{F}$ , is not accepted in the answer field. The answer field must contain only the number $3$ .

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Step-by-step solution

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