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A capacitor is connected to batteries by Nichrome wires and allowed to charge completely. Then the plates are suddenly moved farther apart. Describe what happens and explain in detail why it happens, based on fundamental physical principles. If you give a direction for a current, state whether you are describing electron current or conventional current. Include appropriate diagrams to support your explanation.

Short Answer

Expert verified

The spacing between the plates increases, the capacitance reduces, and the current direction is reversed.

Step by step solution

01

Write the given data from the question.

The distance between the plates of the capacitor is increased when capacitor is completely charged.

02

Determine the formula to describe the given situation.

The capacitance of the capacitor is given by the ratio of the product of area of plates and permeability of space and spacing between the plates.

The expression to calculate the value of the capacitor is given as follows

C=A0d

Here, is the spacing between the plates, is the area of plates and is the permeability of the space.

03

Describe the given situation.

The initial value of the capacitance is given by,

C1=A0d1 鈥︹ (i)

Here, is the initial distance between the plates.

Consider the circuit given below in which the direction of the conventional current is shown by the arrows.

Let鈥檚 assume the plates are separated by the new spacing . The capacitance is given by,

C2=A0d2 鈥︹ (ii)

Here, d2is the new distance between the plates.

From equations (i) and (ii), it is clear that the capacitance is inversely proportional to the spacing between the plates.

The capacitor plates move away, and the distance between plates increases, reducing capacitance. Since in both cases, capacitance is connected with the same voltage, due to which the current flows back to the power supply to restore the voltage.

Therefore, the current starts to flow in the reverse direction, and the arrows show the direction of the conventional current.

Hence when the spacing between the plates is increases the capacitance reduces and direction of the current get reversed.

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Most popular questions from this chapter

Using thick connecting wires that are very good conductors, a Nichrome wire (鈥渨ire 1鈥) of length L1 and cross-sectional area A1 is connected in series with a battery and an ammeter (this is circuit 1). The reading on the ammeter is I1. Now the Nichrome wire is removed and replaced with a different wire (鈥渨ire 2鈥), which is 2.5 times as long and has 5.5 times the cross-sectional area of the original wire (this is circuit 2). In the following question, a subscript 1 refers to circuit 1, and a subscript 2 refers to circuit 2. It will be helpful to write out your solutions to the following questions algebraically before doing numerical calculations. (Hint: Think about what is the same in these two circuits.)(a) What is the value of I2/ I1, the ratio of the conventional currents in the two circuits? (b) What is the value of R2/ R1, the ratio of the resistances of the wires? (c) What is the value of E2/ E1, the ratio of the electric fields inside the wires in the steady states?

Work and energy with a capacitor: A capacitor with capacitance Chas an amount of charge q on one of its plates, in which case the potential difference across the plates is 螖痴=q/C (definition of capacitance). The work done to add a small amount of charge dq when charge the capacitor is dq螖痴=dqq/C. Show by integration that the amount of work required to charge up the capacitor from no charge to final charge Q is 12(Q2/C). Since this is the amount of work required to charge the capacitor, it is also the amount of energy stored in the capacitor. Substituting Q=C螖痴, we can also express the energy as 12C螖痴2.

Consider a copper wire with a cross-sectional area of 1 mm2 (similar to your connecting wires ) and carrying 0.3 A of current, which is about what you get in a circuit with a thick-filament bulb and two batteries in series. Calculate the strength of the very small electric field required to drive this current through the wire.

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).

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.

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