In: Physics

A 1.2 nF parallel-plate capacitor has an air gap between its plates. Its capacitance increases by 3.0 nF when the gap is filled by dielectric. What is the dielectric constant of that dielectric?

The capacitance of the capacitor when the gap

between the plates filled with dielectric is

$$ \begin{aligned} C &=C_{0}+3.0 \mathrm{nF} \\ &=1.2 \mathrm{nF}+3.0 \mathrm{nF} \\ &=4.2 \mathrm{nF} \end{aligned} $$

the capacitance of the parallel plate capacitor

without dielectric is

$$ C_{0}=\frac{\varepsilon_{0} A}{d} $$

the capacitance of the parallel plate capacitor

with dielectric is

$$ C=\frac{K \varepsilon_{0} A}{d} $$

Hence, the dielectric constant of that dielectric is,

$$ K=\frac{C}{C_{0}}=\frac{4.2 \mathrm{nF}}{1.2 \mathrm{nF}}=3.5 $$

Latest Questions

- Match the following properties of liquids to what they indicate about the relative strength of the intermolecular forces in that liquid.
- Rank each satellite based on the net force acting on it. Rank from largest to smallest.
- Complete the following program skeleton. When finished, the program will ask the user for a length (in inches), convert that value to centimeters, and display the result. You are to write the function convert.
- Write a function that accepts an int array and the array's size as arguments.
- The figure below shows a cross section across a diameter of a long cylindrical conductor
- The two 10-cm-long parallel wires in the figure are separated by 5.0 mm.
- What visible wavelengths of light are strongly reflected from a 390-nm-thick soap bubble?