Calculate the capacitance needed to store 10 kWh of energy at 1000 V and the energy stored in a 1.0 m3 volume of air with an electric field of 15 V/m.

Right Em_Legend, let's go. Problem 1: To find the capacitance required, we use the formula for energy stored in a capacitor. Step 1: Convert the energy from kilowatt-hours (kWh) to Joules (J). U = 10 kWh × 3.6 × 10^6 J1 kWh U = 3.6 × 10^7 J Step 2: Use the formula for energy stored in a capacitor, U = (1)/(2)CV^2, and rearrange it to solve for capacitance C. C = (2U)/(V^2) Step 3: Substitute the given values for energy (U) and potential difference (V). C = 2 × 3.6 × 10^7 J(1000 V)^2 C = 7.2 × 10^7 J1 × 10^6 V^2 C = 72 F The required capacitance is 72 F. Problem 2: To find the energy stored in a volume of air due to an electric field, we first calculate the energy density. Step 1: Calculate the energy density (u) using the formula u = (1)/(2) E^2. For air, the permittivity is approximately equal to the permittivity of free space _0 = 8.85 × 10^-12 F/m. u = (1)/(2) _0 E^2 u = (1)/(2) (8.85 × 10^-12 F/m) (15 V/m)^2 u = (1)/(2) (8.85 × 10^-12 F/m) (225 V^2/m^2) u = 9.95625 × 10^-10 J/m^3 Step 2: Multiply the energy density by the given volume to find the total energy stored. U = u × Volume U = (9.95625 × 10^-10 J/m^3) × (1 m^3) U = 9.95625 × 10^-10 J The energy stored is 9.96 × 10^-10 J. Problem 3: To calculate the capacitance of a parallel plate capacitor with a dielectric, we use the formula C = ( _0 A)/(d). Step 1: Identify the given values and constants. Area (A) = 1 m² Distance (d) = 8.8 × 10^-12 m Dielectric constant () = 5 (assuming "factors 0r 5" means =5) Permittivity of free space (_0) = 8.85 × 10^-12 F/m Step 2: Substitute these values into the capacitance formula. C = ( _0 A)/(d) C = 5 × (8.85 × 10^-12 F/m) × (1 m^2)8.8 × 10^-12 m Step 3: Calculate the capacitance. C = 44.25 × 10^-12 F8.8 × 10^-12 C ≈ 5.028 F The capacitance is approximately 5.03 F. Send me the next one 📸