Question 505: Electrostatics & Capacitance

Question

A parallel plate capacitor with air medium between the plates has a capacitance of $$10 \mu \mathrm{F}$$. The area of capacitor is divided into two equal halves and filled with two media (as shown in figure) having dielectric constant $$K_1=2$$ and $$\mathrm{K}_2=4$$. The capacitance of the system will be

Accepted Answer

$$\mathrm{C}=\frac{\varepsilon_0 \mathrm{~A}}{\mathrm{~d}}=10 \mu \mathrm{F}$$
After dividing the area into two equal halves, the resultant capacitance is calculated as,
$$\begin{aligned}
\mathrm{C}_{\mathrm{eq}} & =\mathrm{C}_1+\mathrm{C}_2 \
& =\frac{\mathrm{K}_1 \varepsilon_0 \mathrm{~A}_1}{\mathrm{~d}}+\frac{\mathrm{K}_1 \varepsilon_0 \mathrm{~A}_1}{\mathrm{~d}}=\frac{\frac{2 \varepsilon_0 \mathrm{~A}}{2}}{\mathrm{~d}}+\frac{\frac{4 \varepsilon_0 \mathrm{~A}}{2}}{\mathrm{~d}} \
	herefore \quad \mathrm{C}_{	ext {eq }} & =\frac{\varepsilon_0 \mathrm{~A}}{\mathrm{~d}}+\frac{2 \varepsilon_0 \mathrm{~A}}{\mathrm{~d}}=\frac{3 \varepsilon_0 \mathrm{~A}}{\mathrm{~d}}=3 	imes 10=30 \mu \mathrm{F}
\end{aligned}$$

Answer

10 $$\mu$$F

Answer

20 $$\mu$$F

Answer

30 $$\mu$$F

Answer

40 $$\mu$$F

Electrostatics & Capacitance

A parallel plate capacitor with air medium between the plates has a capacitance of $10 \mu \mathrm{F}. The area of capacitor is divided into two equal halves and filled with two media (as shown in figure) having dielectric constant K_1=2 and \mathrm{K}_2=4$. The capacitance of the system will be

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