A particular capacitor is initially charged. Then a high-resistance Nichrome wire is connected between the plates of the capacitor, as shown in Figure 19.69. The needle of a compass placed under the wire deflects 20°to the east as soon as the connection is made. After 60sthe compass needle no longer deflects.

(a)Which of the diagrams in Figure 19.69 best indicates the electron current at three locations in this circuit? (1) 0.01safter the circuit is connected, (2) 15s after the circuit is connected, (3) 120s after the circuit is connected.

(b)Which of the diagrams in Figure 19.70 best indicates the net electric field inside the wire at three locations in this circuit? (1) 0.01s after the circuit is connected, (2) 15safter the circuit is connected, (3) 120s after the circuit is connected.

Short Answer

Expert verified

(a) (1) Figure (C) best depicts the current in the circuit after0.01s.

(2) Figure (B) best depicts the current in the circuit after15s.

(3) Figure (A) best depicts the current in the circuit after 120s.

Step by step solution

01

Given data

A fully charged capacitor is connected to a Nichrome wire. The magnetic deflection under the wire stops after 60s.

02

Discharging of a capacitor

When a fully charged capacitor is connected in a circuit, electron flows from the negative to the positive plate, thus reducing charge in both plates.

03

(a) Determination of the current in the circuit at different times

As charges flow from the negative plate to the positive plate through the circuit, the net charge in the plates reduces. With decrease in charge of the plates, the fringe field in the circuit decreases thus decreasing the current. This continues till the capacitor is completely discharged and the current in the circuit is zero. Evidently this happens at when there is no further deflection in the magnetic needle. Thus at the discharging has begun and the current is maximum. This is best depicted by figure (C). After the discharging has continued for a while and the current has reduced. This is best depicted by figure (B). After the capacitor is completely discharged and the current is zero. This is best depicted by figure (A).

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Most popular questions from this chapter

How is the charging time for a capacitor correlated with the initial current? That is, if the initial current is bigger, is the charging time, longer, shorter, or the same?

The capacitor in Figure 19.68 is initially uncharged, then the circuit is connected. Which graph in Figure 19.66 best describes the magnitude of the fringe field of the capacitor at location A(inside the connecting wire) as a function of time?

A long Iron slab of width w and height h emerges from a furnace, as shown in Figure 19.79. Because the end of the slab near the furnace is hot and the other end Is cold, the electron mobility increases significantly with the distance x. The electron mobility is u=u0+kxwhere u0is the mobility of the iron at the hot end of the slab. There are n iron atoms per cubic meter, and each atom contributes one electron to the sea of the mobile electron (we can neglect the small thermal expansion of the iron). A steady state conventional current runs through the slab from the hot end towards cold end, and an ammeter (not shown) measures the current to have a magnitude I in amperes. A voltmeter is connected to two locations a distance d apart, as shown. (a) Show the electric field inside the slab at two locations marked with ×. Pay attention to the relative magnitudes of the two vectors that you draw. (b) Explain why the magnitude of the electric field is different at these two locations. (c) At a distance x from the left voltmeter connection, what is the magnitude of the electric field in terms x and the given quantities w,h,d,u0,k,l, and n ( and fundamental constants)? (d) What is the sign of potential difference displayed on the voltmeter? Explain briefly. (e) In terms of the given quantitiesw,h,d,u0,k,l, and n and ( and fundamental constants), what is the magnitude of the voltmeter reading? Check your work. (f) What is the resistance of this length of the iron slab?

A circuit consists of two batteries (with negligible resistance), six ohmic resistors and connecting wires that have negligible resistance. The resistance R1is 10Ω, R2 is 20Ω, R3 is 30Ω, R4is 12Ω, R5is 15Ω and R6 is 20Ω. Unknown currents I1,I2 ,I3 ,I4 , I5 and I6 have their directions marked on the circuit diagram in figure 19.87.

(a) Write down a set of equations that could be solved for the six unknown currents. Make sure you can explain how to you got these equations. (b) When a correct set of equations is solved the currents are as follows (to the nearest miiampeares) I1=0.4394A, I2=0.3312A, I3=0.0065A, I4=0.1082A, I5=0.3247Aand I6=0.4329A. Check your equations by substituting in these numbers. (c) Suppose that you connect the negative lead of a voltmeter to location C. What does the voltmeter read, including both magnitude and sign? (d) What does the power output of the 5 V battery? (e) Resistor is made of a very thin metal wire that is 3 mm long, with a diameter of 0.1 mm. What is the electric field inside the metal resistor.

A circuit consists of a battery, whose emf is K, and five Nichrome wires, three thick and two thin as shown in Figure 19.78. The thicknesses of the wires have been exaggerated in order to give you room to draw inside the wires. The internal resistance of the battery is negligible compared to the resistance of the wires. The voltmeter is not attached until part (e) of the problem. (a) Draw and label appropriately the electric field at the locations marked × inside the wires, paying attention to appropriate relative magnitudes of the vectors that you draw. (b) Show the approximate distribution of charges for this circuit. Make the important aspects of the charge distribution very clear in your drawing, supplementing your diagram if necessary with very brief written descriptions on the diagram. Make sure that parts (a) and (b) of this problem are consistent with each other. (c) Assume that you know the mobile-electron density n and the electron mobility u at room temperature for Nichrome. The lengths (L1,L2,L3)and diameters (d1,d2)of the wires are given on the diagram. Calculate accurately the number of electrons that leave the negative end of the battery every second. Assume that no part of the circuit gets very hot. Express your result in terms of the given quantities (K,L1,L2,L3,d1,d2,nandu). Explain your work and identify the principles you are using. (d) In the case that d2d1, what is the approximate number of electrons that leave the negative end of every second? (e) A voltmeter is attached to the circuit with its + lead connected to location B (halfway along the leftmost thick wire) and its - lead connected to location C (halfway along the leftmost thin wire). In the case that d2d1, what is the approximate voltage shown on the voltmeter, including sign? Express your result in terms of the given quantities (K,L1,L2,L3,d1,d2,nandu).

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