MOSFETs: Modeling and Characteristics

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Questions and Answers

If a regular polygon has 8 sides, which calculation determines the measure of each interior angle in degrees?

  • $180 - (360/8)$
  • $(8-2) * 180 / 8$ (correct)
  • $360/8$
  • $(8-2) * 180$

A circle has a radius of 7 cm. Which calculation would determine the area of a sector with a central angle of 45 degrees?

  • $(45/360) * Ï€ * 7^2$ (correct)
  • $(45/360) * 2 * Ï€ * 7$
  • $(45/360) * 7^2$
  • $Ï€ * 7^2$

A right rectangular prism has dimensions length = 8, width = 6, and height = 4. Which calculation gives the surface area?

  • $(8 * 6) + (8 * 4) + (6 * 4)$
  • $2 * (8 + 6 + 4)$
  • $(2 * 8) + (2 * 6) + (2 * 4)$
  • $2 * ((8 * 6) + (8 * 4) + (6 * 4))$ (correct)

If a square pyramid has a base side length of 6 and a height of 4, what is the volume of the pyramid?

<p>$48$ (D)</p>
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A cylinder has a radius of 5 and a height of 10. Which of the following calculations would determine its lateral area?

<p>$2 * π * 5 * 10$ (C)</p>
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A cone has a radius of 3 and a slant height of 5. Which calculation determines the surface area of the cone?

<p>$π * 3^2 + π * 3 * 5$ (D)</p>
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If a sphere has a radius of 6, which calculation gives the volume of the sphere?

<p>$(4/3) * π * 6^3$ (A)</p>
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If a hemisphere has a radius of 4, which calculation determines its surface area?

<p>$3 * π * 4^2$ (A)</p>
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A parallelogram has a base of 10 and a height of 5. What is its area?

<p>50 (A)</p>
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A trapezoid has bases of length 6 and 8 and a height of 4. Which calculation will determine the area of the trapezoid?

<p>$(1/2) * 4 * (6 + 8)$ (C)</p>
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A rhombus has diagonals of length 12 cm and 5 cm. What is the area of the rhombus?

<p>30 $cm^2$ (A)</p>
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A hexagonal prism has a base area of 50 $cm^2$ and a height of 10 cm. What is the volume of the prism?

<p>500 $cm^3$ (D)</p>
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A triangular prism has a base area of 25 $cm^2$, a perimeter of 30 cm, and a height of 8 cm. What is the total surface area?

<p>290 $cm^2$ (B)</p>
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If the perimeter of the base of a square pyramid is 20, and the slant height is 8, what is the lateral area of the pyramid?

<p>80 (A)</p>
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What formula calculates the volume of a cylinder?

<p>$V = πr^2h$ (B)</p>
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If a cone has a radius of 4 and a height of 6, which calculation gives its volume?

<p>$(1/3) * π * 4^2 * 6$ (D)</p>
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A cylinder has a radius of 3 and a height of 7. Which formula would determine its surface area?

<p>$2Ï€r^2 + 2Ï€rh$ (D)</p>
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A rectangular prism has a length of 5, a width of 4, and a height of 3. Determine the volume.

<p>60 (C)</p>
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A cone has a surface area of $40Ï€$ and a radius of 4. What is the slant height of the cone?

<p>6 (A)</p>
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Flashcards

Area of a Parallelogram

Area = (base) x (height)

Area of a Trapezoid

Area = 1/2 x height x (base1 + base2)

Area of a kite or rhombus

Area = 1/2 x (diagonal 1) x (diagonal 2)

Regular Polygon Angle

Central Angle = 360 / number of sides

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Area of Regular Polygon

A = (1/2) x ap, where 'a' is the apothem and P is perimeter.

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Area Of a Circle

Area = pi x r^2

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Area of a circular sector

A = (m/360) x (pi x r^2)

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Pyramids surface area

LA = (1/2)lP, where l = slant height, P = perimeter of base. SA= (1/2)lP + B, where B = bh

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Cone surface area

LA = pi x r x l, where l = slant height. SA = pi x r^2 + pi x r x l

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Surface Area of a Rectangular Prism

SA = 2lw + 2lh + 2wh or SA = LA + 2(Base A)

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All other prism surface area

LA=hp, SA = hp + 2B, where h= height between bases, p = perimeter of the base, B = area of the base

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Cylinder Surface Area

LA = 2 x pi x r x h , SA = 2 x pi x r^2 + 2 x pi x r x h

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Volume of a Rectangular Prism

V = lwh

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Volume of all other prism

V = Bh, B= base area, h = height between bases

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Volume of a Pyramid

V = (1/3) x B x h, where B = area of the base and h is the height

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Volume of a Cone

V = (1/3) x pi x r^2 x h

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Volume of a Cylinder

V = pi x r^2 x h

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Sphere Volume and Surface Area

V = (4/3) x pi x r^3, SA = 4 x pi x r^2

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Hemisphere Volume and Surface Area

V = (2/3) x pi x r^3 , SA = 3 x pi x r^2

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Area of a rectangle

Area = base x height

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Study Notes

Lecture 17 Summary

  • MOSFETs are essential circuit elements in electronics
  • Classical electrostatics dictates that the mobile charge in channel is equal to negative of the surface charge, which is proportional to the gate voltage relative to threshold voltage scaled by the gate oxide capacitance: $Q_i = -Q_s = C_{OX}(V_{GS} - V_T)$
  • A simple MOSFET model relates drain current to gate and drain voltages
  • For small $V_{DS}$, the drain current is: $I_D = \mu_n C_{OX} \frac{W}{L} (V_{GS} - V_T) V_{DS}$
  • In saturation, the drain current is: $I_D = \mu_n C_{OX} \frac{W}{2L} (V_{GS} - V_T)^2$
  • The simple MOSFET model captures essential characteristics, but it has many limitations

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