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What current flows through a 2.54-cm-diameter rod of pure silicon that is 20 cmlong, when1.00×103Vis applied to it? (Such a rod may be used to make nuclear-particle detectors, for example.)

Short Answer

Expert verified

The current in the rod is obtained as: 1.10 mA .

Step by step solution

01

Define Resistance

In an electrical circuit, resistance is a measure of the resistance to current flow. The Greek letter omega(Ω)is used to represent resistance in ohms.

02

Concepts and Principles

Ohm's Law: The current Ithrough a circuit element (other than the battery) can be determined by dividing the potential difference Vwhich is across the circuit element by its resistanceR :

I=VR

The electrical resistance of the value Rof a resistive circuit element depends on its geometric structure (its length symbolized as Land cross-sectional area symbolized as ) and on the resistivity ρof the material of which it is made:

R=ρLA

03

The given data

  • The diameter of the rod is:D=2.54cm×1m100cm=0.0254m.
  • The radius of the rod is:r=D/2=0.0127m.
  • The length of the rod is:L=20.0cm×1m100cm=0.200m.
  • The voltage applied to the rod is:V=1.00×103V.
  • The resistivity of silicon is: ρ=2300Ω·m.
04

Evaluating the current in the rod

The current in the rod can be calculated as:

I=VρLπr2

Entering the values, we obtain:

I=1.00×103V2300Ω·m×0.200mπ0.0127m2=1.10×10-3A=1.10×10-3A×1000.mA1A=1.10mA

Therefore,the current in the rod is: data-custom-editor="chemistry" 1.10mA.

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