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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

Expert verified

The current stays more nearly constant in the circuit with capacitor

Step by step solution

01

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.

02

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=E0AKd

Here, Ais the area of the plates, Kis the dielectric constant and dis the separation between the plates.

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

Q=C△V…… (i)

Here, â–³Vis the potential difference between the plates of capacitor.

03

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

Calculate the charge on the plates of the capacitors.

Substitute E0AKdforC into equation (i).

Q=E0AKdâ–³V

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 .

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Most popular questions from this chapter

A battery with negligible internal resistance is connected to a resistor. The power produced in the battery and power dissipated in the resistor are both P1. Another resistor of same kind is added, so circuit consists of a battery and two resistors in series. (a) in terms of P1 how much power is dissipated in the first resistor ? . (a) in terms of P1 how much power is produced in the battery ? (c ) The circuit is rearranged so that the two resistors are in parallel rather than in series. In terms of P1, now how much power is produced in the battery?

1/KThe charge on an isolated capacitor does not change when a sheet of glass is inserted between the capacitor plates, and we find that the potential difference decreases (because the electric field inside the insulator is reduced by a factor of 1/K ). Suppose instead that the capacitor is connected to a battery, so that the battery tries to maintain a fixed potential difference across the capacitor. (a) A light bulb and an air-gap capacitor of capacitanceC are connected in series to a battery with known emf. What is the final chargeQ on the positive plate of the capacitor? (b) After fully charging the capacitor, a sheet of plastic whose dielectric constantK is inserted into the capacitor and fills the gap. Does any current run through the light bulb? Why? What is the final charge on the positive plate of the capacitor?

How is the initial current through a bulb affected by putting a capacitor in series in the circuit? Explain briefly.

Suppose that you charges a 2.5 Fcapacitor with two 1.5 Vbatteries. How much charge would be on each plate in the final state? How many excess electrons would be on the negative plate?

For the circuit shown in figure 19.86, which consists of batteries with known emf and ohmic resistors with known resistance, write the correct number of energy-conservation and current node rule equations that would be adequate to solve for the unknown currents, but do not solve the equations. Label nodes and currents on the diagram, and identify each equation (energy or current, and for which loop or node).

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