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Chapter 19: Q57P (page 799)

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.

Short Answer

Expert verified

The strength of the very small electric field required to drive this current through the wire is 5×10-3V/m.

Step by step solution

01

Given data

The data can be listed as,

  • The cross-sectional area of copper wire is, A=1mm2=1×10-6m2.
  • Current is, I=0.3A.
02

Concept

If a current flows in the circuit, it is influenced by many factors, such as the length of the wire, the cross-sectional area of the wire, and the applied voltage on the wire.

03

Determination of the required electric field

The wire is made of copper metal only.

The required electric field can be determined using the formula as,

E=ρIA

Here ρis the resistivity of the copper wire whose value is 16.78×10-9Ω·m.

Substitute the values in the above expression, and we get,

E=16.78×10-9Ω·m0.3A1×10-6m2=5.03×10-3Ω·m-1·A~5×10-3V/m

Thus, the strength of the very small electric field required to drive this current through the wire is 5×10-3V/m.

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Most popular questions from this chapter

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?

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.

In the circuit shown in Figure 19.77 the emf of the battery is 7.4V. Resistor R1has a resistance of 31Ω, resistor R2 has a resistance of 47Ω, and resistor R3has a resistance of 52Ω . A steady current flows through the circuit.

(a)What is the equivalent resistance of R1and R2 ? (b) What is the equivalent resistance of all three resistors? (c) What is the conventional current throughR3

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).
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