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

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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

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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

Waves Physics

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Electric Charge Field and Potential

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.