Question

The insulating layer between the plates of a capacitor not only holds the plates apart to prevent conducting contact but also has a big effect on charging. Consider two capacitors whose only difference is that capacitor number has nothing between the plates, while capacitor number has a layer of plastic in the gap (Figure 19.57). They are placed in two different circuits having similar batteries and bulbs in series with the capacitor.

Show that in the first fraction of a second the current stays more nearly constant (decreases less rapidly) in the circuit with capacitor number . Explain your reasoning in detail. Hint: Consider the electric fields produced in the nearby wires by this plastic-filled capacitor. Suppose that the plastic is replaced by a different plastic that polarizes more easily. In the same circuit, would this capacitor keep the current more nearly constant or less so than capacitor ?

A more extensive analysis shows that this trend holds true for the entire charging process: the capacitor containing an easily polarized insulator ends up with more charge on its plates. The capacitor you have been using is filled with an insulator that polarizes extremely easily.

Short answer

The current stays more nearly constant in the circuit with capacitor

Step-by-step solution

Write the given data from the question.

Capacitor has nothing between the plates.

Capacitor has layer of plastic between the plates.

The circuit has the same battery and bulb in the series with the capacitor.

Determine the formulas to show that the current stays more nearly constant) in the circuit with capacitor number .  

The expression to calculate the capacitor when it is filled with the dielectric material is given as follows.

$C=\frac{E_{0}AK}{d}$

Here, $A$is the area of the plates, $K$is the dielectric constant and $d$is the separation between the plates.

The expression to calculate the charge on the plates is given as follows.

$Q=C△V$…… (i)

Here, $△V$is the potential difference between the plates of capacitor.

Show that the current stays more nearly constant in the circuit with capacitor number .  

Calculate the charge on the plates of the capacitors.

Substitute $\frac{E_{0}AK}{d}$for$C$ into equation (i).

$Q=\frac{E_{0}AK}{d}△V$

From the above equation, it is clear that the charge on the capacitor plates depends on the dielectric material placed between them.

The dielectric field reduces the strength of the electric field, and by keeping the total charge constant on the plates, the potential difference is reduced. The capacitance of the capacitor increases.

Therefore, the capacitance of capacitor and the charge on capacitor is more than capacitor . Due to more charge, equilibrium is reached, and the magnitude of the fringe field is enough to cancel the other fields.

Hence the current stays more nearly constant in the circuit with capacitor .