Q. 14 聽 a. Evaluate VR聽 in 聽figure ... [FREE SOLUTION]

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Chapter 32: Q. 14 (page 924)

a. Evaluate $V_{R}$ in figure at emf frequencies $100, 300, 1000, 3000, 10000 H z$
b. Graph $V_{R}$ versus frequency. Draw a smooth curve through your five points.

Short Answer

Expert verified

Part(a) $V_{R}$ at emf frequencies $100, 300, 1000, 3000, 10000$ are $1.00, 2.90, 7.11, 9.47, 9.97 V$ respectively.

Part(b) Required figure is given below.

Step by step solution

Part(a) Step 1: Given information

We have given different frequencies

$100, 300, 1000, 3000, 10000$ and $R = 100 惟, E_{0} = 10 V, C = 1.6 脳 10^{- 3} F$

We have to find $V_{R}$

Part(a) Step 2 : Simplify

As we know,

$V_{R} =$ voltage across resistor

$R =$ resistance

$C =$ capacitance

$f =$ frequency

$X_{C} =$ capacitive reactance

${鈭�}_{鈭�} =$ emf

$V_{R} = I R I = \frac{螘_{0}}{\sqrt{R^{2} + X_{C}^{2}}} X_{C} = \frac{1}{W C} = \frac{1}{2 蟺 f C}$

Now if

a. $f = 100 H z V_{R} = \frac{{鈭�}_{鈭�}}{\sqrt{R^{2} + \frac{1}{{(2 蟺 f C)}^{2}}}} = \frac{10}{\sqrt{100^{2} + \frac{1}{{(2 蟺 (100) (1.6 脳 10^{- 3}))}^{2}}}} V_{R} = 1.00 V f = 300 H z V_{R} = \frac{{鈭�}_{鈭�}}{\sqrt{R^{2} + \frac{1}{{(2 蟺 f C)}^{2}}}} = \frac{10}{\sqrt{100^{2} + \frac{1}{{(2 蟺 (300) (1.6 脳 10^{- 3}))}^{2}}}} V_{R} = 2.90 V f = 1000 H z V_{R} = \frac{{鈭�}_{鈭�}}{\sqrt{R^{2} + \frac{1}{{(2 蟺 f C)}^{2}}}} = \frac{10}{\sqrt{100^{2} + \frac{1}{{(2 蟺 (1000) (1.6 脳 10^{- 3}))}^{2}}}} V_{R} = 7.11 V f = 3000 H z V_{R} = \frac{{鈭�}_{鈭�}}{\sqrt{R^{2} + \frac{1}{{(2 蟺 f C)}^{2}}}} = \frac{10}{\sqrt{100^{2} + \frac{1}{{(2 蟺 (3000) (1.6 脳 10^{- 3}))}^{2}}}} V_{R} = 9.47 V f = 10000 H z V_{R} = \frac{{鈭�}_{鈭�}}{\sqrt{R^{2} + \frac{1}{{(2 蟺 f C)}^{2}}}} = \frac{10}{\sqrt{100^{2} + \frac{1}{{(2 蟺 (10000) (1.6 脳 10^{- 3}))}^{2}}}} V_{R} = 9.97 V$

Part(b) Step 1: Given information

We have to draw graph $V_{R}$ vs frequencies

Part(b) Step 2 : Simplify

Graph:

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91影视

a. Evaluate $V_{R}$ in figure at emf frequencies $100, 300, 1000, 3000, 10000 H z$
b. Graph $V_{R}$ versus frequency. Draw a smooth curve through your five points.

Short Answer

Step by step solution

Part(a) Step 1: Given information

Part(a) Step 2 : Simplify

Part(b) Step 1: Given information

Part(b) Step 2 : Simplify

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91影视

a. Evaluate VR in figure at emf frequencies100,300,1000,3000,10000Hzb. Graph VRversus frequency. Draw a smooth curve through your five points.

Short Answer

Step by step solution

Part(a) Step 1: Given information

Part(a) Step 2 : Simplify

Part(b) Step 1: Given information

Part(b) Step 2 : Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Solid State Physics

Work Energy and Power

Geometrical and Physical Optics

Engineering Physics

Waves Physics

Fundamentals of Physics

Study anywhere. Anytime. Across all devices.

a. Evaluate $V_{R}$ in figure at emf frequencies $100, 300, 1000, 3000, 10000 H z$
b. Graph $V_{R}$ versus frequency. Draw a smooth curve through your five points.