Calculate the energy a parallel plate capacitor (charged to a voltage of V=12V) with plate area A = 2m2…

Question

Calculate the energy a parallel plate capacitor (charged to a voltage of V=12V) with plate area A = 2m2, plate separation d = 0.02m, and vacuum permittivity ε₀ = 8.854 × 10⁻¹² F/m.

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QUESTION ONE

b) Calculate the energy a parallel plate capacitor (charged to a voltage of $V=12\text{V}$ ) with the following:

Plate area $A = 2\text{m}^2$
Plate separation $d = 0.02\text{m}$
Vacuum permittivity $\epsilon_0 = 8.854 \times 10^{-12}\text{ F/m}$

Calculate the capacitance $C$ of the parallel plate capacitor.
The formula for the capacitance of a parallel plate capacitor in vacuum is:
$C = \frac{\epsilon_0 A}{d}$
Substitute the given values:
$C = \frac{(8.854 \times 10^{-12}\text{ F/m}) \times (2\text{ m}^2)}{0.02\text{ m}}$ $C = \frac{17.708 \times 10^{-12}}{0.02}\text{ F}$ $C = 885.4 \times 10^{-12}\text{ F}$ $C = 885.4\text{ pF}$
Calculate the energy $W_e$ stored in the capacitor.
The formula for the energy stored in a capacitor is:
$W_e = \frac{1}{2} C V^2$
Substitute the calculated capacitance $C$ and the given voltage $V$ :
$W_e = \frac{1}{2} \times (885.4 \times 10^{-12}\text{ F}) \times (12\text{ V})^2$ $W_e = \frac{1}{2} \times (885.4 \times 10^{-12}) \times 144\text{ J}$ $W_e = 442.7 \times 10^{-12} \times 144\text{ J}$ $W_e = 63748.8 \times 10^{-12}\text{ J}$

Calculate the energy a parallel plate capacitor (charged to a voltage of V=12V) with plate area A = 2m2, plate separation d = 0.02m, and vacuum permittivity ε₀ = 8.854 × 10⁻¹² F/m.

Step-by-step solution

Calculate the capacitance $C$ of the parallel plate capacitor.

Calculate the energy $W_e$ stored in the capacitor.

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More Physics Questions

Calculate the energy a parallel plate capacitor (charged to a voltage of V=12V) with plate area A = 2m2, plate separation d = 0.02m, and vacuum permittivity ε₀ = 8.854 × 10⁻¹² F/m.

Step-by-step solution

Calculate the capacitance CCC of the parallel plate capacitor.

Calculate the energy WeW_eWe​ stored in the capacitor.

Still stuck on this one?

More Physics Questions

Calculate the capacitance $C$ of the parallel plate capacitor.

Calculate the energy $W_e$ stored in the capacitor.