Question

Suppose that instead of placing an insulating layer between the plates of the capacitor shown in Figure 19.57, you inserted a metal slab of the same thickness, just barely not touching the plates. In the same circuit, would this capacitor keep the current more nearly constant or less so than capacitor 2 in Question Q4? Explain why this is essentially equivalent to making a capacitor with a shorter distance between the plates.

Short answer

This circuit keeps constant more nearly constant than capacitor with the plastic plate of Question 4.

Step-by-step solution

Write the given data from the question.

The metal slab is inserted between the plates of the capacitor that makes some distance from the plates.

Determine the formulas to find out if capacitor keep the current more nearly constant or less so than capacitor 2 in Question Q4.

The expression to calculate the capacitance of the capacitor is given as follows.

$C=\frac{A{E}_0}{d}$

Here, is the area of the plates, and is the separation between the plates.

Find out if capacitor keep the current more nearly constant or less so than capacitor 2 in Question Q4.

Consider the figure after placing the metal slab between the plates of the capacitor.

When the metal slab is placed between the plates of the capacitor, two capacitance is formed in the gaps of the capacitor plates and metal slab, and these two capacitors are in the series, but separation distance is decreased due to the slab which results to increase the value of the capacitance.

The rate of change of the capacitor current is given as follows.

$\frac{dl}{dt}=\frac{I_0}{RC}{e}^{-t/RC}$

Here,$I_0$ is the initial current and$R$ is the resistance.

From the above the capacitance is inversely proportional to the current. As the value of the capacitance increases the current decreases.

Hence this circuit keeps constant more nearly constant than capacitor with the plastic plate of Question 4.