Chapter 32: Q. 13 (page 924)

a. Evaluate $V_{C}$ at emf frequencies $1, 3, 10, 30, 100 K H z$
b. Graph $V_{C}$ versus frequency. Draw a smooth curve through your five points.

Short Answer

Expert verified

Part(a) $V_{C}$ at emf frequencies $1, 3, 10, 30, 100 K H z$ are $9.94, 9.57, 7.05, 3, 15, 0.99 V$ respectively.

Part(b) Required figure is given below.

Step by step solution

Part(a) Step 1 : Given information

We are given various frequencies $1, 3, 10, 30, 100 K H z$ . with Capacitance of $1.0 μ F$ , Resistance of $16 Ω$ , Emf of $10 V (\cos (w t))$

We have to find $V_{c}$

Part(a) Step 2 : Simplify

As we know,

$V_{c} = I X_{c}$

$V_{C} =$ voltage across capacitor

$f =$ frequency

$R =$ resistance

$C =$ capacitance

$\in_{\circ} =$ emf

Where, the capacitive reactance is

$X_{c} = \frac{1}{w C} = \frac{1}{2 π f C}$

Now,

the peak current is

$I = \frac{\in_{0}}{\sqrt{R^{2} + X_{C}^{2}}}$

$V_{C} = \frac{\in_{\circ}}{\sqrt{1 + {(2 π f R C)}^{2}}}$

If $f = 1 K H z$

$V_{c} = \frac{10}{\sqrt{1 + {(2 π (1) (16) (1 \times 10^{- 3}))}^{2}}} = 9.94 V$

If $f = 3 K H z$

$V_{C} = \frac{10}{\sqrt{1 + {(2 π (3) (16) (1 \times 10^{- 3}))}^{2}}} = 9.57 V$

If $f = 10 K H z$

$V_{C} = \frac{10}{\sqrt{1 + {(2 π (10) (16) (1 \times 10^{- 3}))}^{2}}} = 7.05 V$

If $f = 30 K H z$

$V_{C} = \frac{10}{\sqrt{1 + {(2 π (30) (16) (1 \times 10^{- 3}))}^{2}}} = 3.15 V$

If $f = 100 K H z$

$V_{C} = \frac{10}{\sqrt{1 + {(2 π (100) (16) (1 \times 10^{- 3}))}^{2}}} = 0.99 V$

Part(b) Step 1 : Given information

We have to draw graph between $V_{C}$ vs Frequencies

Part(b) Step 2 : Simplify

Graph

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

a. Evaluate $V_{C}$ at emf frequencies $1, 3, 10, 30, 100 K H z$
b. Graph $V_{C}$ 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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Modern Physics

Magnetism

Electricity and Magnetism

Astrophysics

Wave Optics

Mechanics and Materials

Study anywhere. Anytime. Across all devices.

a. Evaluate VCat emf frequencies 1,3,10,30,100KHzb. Graph VCversus 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

Modern Physics

Magnetism

Electricity and Magnetism

Astrophysics

Wave Optics

Mechanics and Materials

Study anywhere. Anytime. Across all devices.

a. Evaluate $V_{C}$ at emf frequencies $1, 3, 10, 30, 100 K H z$
b. Graph $V_{C}$ versus frequency. Draw a smooth curve through your five points.