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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 net electric field at location A (inside the connecting wire) as a function of time?

Short Answer

Expert verified

Figure (d) best depicts the net electric field at A.

Step by step solution

01

Given data

An uncharged capacitor is connected to a bulb and two batteries in series.

02

Charging of a capacitor

When an uncharged capacitor is connected to a battery, positive charges from the positive end of the battery flow to one plate of the capacitor and start accumulating there and negative charges from the negative end of the battery move to the other plate of the capacitor and start accumulating there.

03

Determination of the graph of the net electric field at A

As charge accumulates on the capacitor plates, the fringe field in the circuit increases. This opposes the battery field. Hence the net field decreases with time. This continues till the fringe field completely cancels out the field due to the battery. At this point the net field is zero. This is best depicted by figure (d).

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Most popular questions from this chapter

When a thin-filament light bulb is connected to two 1.5Vbatteries in series, the current is0.075AWhat is the resistance of the glowing thin-filament bulb?

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 d2≪d1, 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 d2≪d1, 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).

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).

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 d2≪d1, 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 thatd2≪d1 , 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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