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What would be the potential difference VC-VBacross the thin resistor in Figure 18.103 if the battery emf is3.5V ? Assume that the electric field in the thick wires is very small (so that the potential differences along the thick wires are negligible). Do you have enough information to determine the current in the circuit?

Short Answer

Expert verified

The potential difference VC-VBis 3.5Vand the information is not enough to calculate the current in the circuit.

Step by step solution

01

Write the given data from the question.

The emf of the battery,VA-VD=3.5V

The electric field thick wire us very small due to this the potential difference across it is negligible.

The voltage difference,VB-VA0V

The voltage difference,VD-VC=0V

02

Determine the formulas to calculate the potential difference and current in the circuit.

The average drift speed of the mobile electron is given by the product of the electron mobility and electric field.

V=UE 鈥︹ (i)

Here, U is the electron mobility and E is the electric field.

The expression to calculate the current in the circuit is given as follows.

i=nAv 鈥︹ (ii)

Here, A is the area of the wire.

03

Calculate the potential difference and current in the circuit.

According to the Kirchhoff鈥檚 Voltage law, the algebraic sum of the voltage in the circuit is always equal to zero.

V=0(VB-VA)+(VC-VB)+(VD-VC)+(VA-VD)=00+(VC-VB)+0+3.5=0(VC-VB)=-3.5V

The electrical field in the circuit is given by,

E=VL

Derive the expression for the current in the circuit.

SubstituteuE for V into equation (ii).

i=nAuE

SubstituteV/L forE into above equation.

i=nAuVL

From the above equation, it is clear that, to calculate the current in the circuit we need property of the resistor. Therefore, the required information to calculate the current in the circuit is not enough.

Hence, the potential difference VC-VBis 3.5Vand the information is not enough to calculate the current in the circuit.

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Most popular questions from this chapter

In the circuit shown in Figure 18.91, all of the wire is made of Nichrome, but one segment has a much smaller cross-sectional area. On a copy of this diagram, using the same scale for magnitude that you used in the previous question for Figure 18.90, show the steady-state electric field at the locations indicated, including in the thinner segment. Before attempting to answer these questions, draw a copy of this diagram. All of the locations indicated by letters are inside the wire.

(a)On your diagram, show the electric field at the locations indicated, paying attention to relative magnitude. Use the same scale for magnitude as you did in the previous question.

(b)Carefully draw pluses and minuses on your diagram to show the approximate surface charge distribution that produces the electric field you drew. Make your drawing show clearly the differences between regions of high surface charge density and regions of low surface-charge density. Use your diagram to determine which of the following statements about this circuit are true.

(1) There is a large gradient of surface charge on the wire between locations Cand E. (2) The electron current is the same at every location in this circuit.

(3) Fewer electrons per second pass location Ethan location C.

(4) The magnitude of the electric field at location Gis smaller in this circuit than it

was in the previous circuit (Figure 18.90).

(5) The magnitude of the electric field is the same at every location in this circuit.

(6) The magnitude of the electric field at location D is larger than the magnitude of the electric field at location G.

(7) There is no surface charge at all on the wire near location G.

(8) The electron current in this circuit is less than the electron current in the previous circuit (Figure 18.90).

When a single thick-filament bulb of a particular kind and two batteries are connected in series, 31018 electrons pass through the bulb every second. When two batteries in series are connected to a single thin-filament bulb, with a filament made of the same material and length as the thick-filament bulb but a smaller cross-section, only 1.51018 electrons pass through the bulb every second. (a) In the circuit shown in Figure 18.109, how many electrons per second flow through the thin-filament bulb? (b) What approximations or simplifying assumptions did you make? (c) Show approximately the surface charge on a diagram of the circuit.

A Nichrome wire 30 cm long and 0.25 mm in diameter is connected to a 1.5 V flashlight battery. What is the electric field inside the wire? Why you don鈥檛 have to know how the wire is bent? How would your answer change if the wire diameter change were 0.35 mm? (Not that the electric field in the wire is quiet small compared to the electric field near a charged tape.)

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Criticize the statement below on theoretical and experimental grounds. Be specific and precise. Refer to your own experiments, or describe any new experiments you perform: 鈥淎 flashlight battery always puts out the same amount of current, no matter what is connected to it.鈥

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