A capacitor with capacitance $1 \mu \mathrm{~F}$ is connected to a 20 V supply. The distance between the plates is 1 $\mu \mathrm{m}$. Find the energy density between the plates. (Shift - II Memory Based)

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YESPYQ · Accepted Answer

Correct answer: a) $1770 \mathrm{~J} / \mathrm{m}^3$. To find the energy density (energy per unit volume) between the plates of the capacitor, we use the formula: $\text{Energy Density}(u)=\frac{1}{2}{ϵ}_{0}{E}^{2}$ where: ${ϵ}_{0}$​ = Permittivity of free space $=8.85\times 1{0}^{−12}\text{ }F\mathrm{/}m$ $E$ = Electric field inside the capacitor, given by: $E=\frac{V}{d}$​ Step 1: Calculate the Electric Field $E$ $E=\frac{V}{d}=\frac{20V}{1\times 1{0}^{−6}m}$ $E=2\times 1{0}^{7}\text{ }V\mathrm{/}m$ Step 2: Calculate the Energy Density $u$ $u=\frac{1}{2}\times (8.85\times 1{0}^{−12})\times (2\times 1{0}^{7}{)}^{2}$ $u=\frac{1}{2}\times (8.85\times 1{0}^{−12})\times (4\times 1{0}^{14})$ $u=\frac{1}{2}\times 3.54\times 1{0}^{3}$ $u=1.77\times 1{0}^{3}\text{ }J\mathrm{/}{m}^{3}$ Final Answer: $1770J/{m}^{3}$ So, the correct option is (A) 1770 J/m³ .

A capacitor with capacitance \(1 \mu \mathrm{~F}\) is connected to a 20 V supply. The distance between the plates is 1 \…

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