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 $R = 100 Ω, E_{0} = 10 V, C = 1.6 \times 10^{- 3} F$

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

$\in_{\circ} =$ emf

$V_{R} = I R I = \frac{Ε_{0}}{\sqrt{R^{2} + X_{C}^{2}}} X_{C} = \frac{1}{W C} = \frac{1}{2 π f C}$

Now if

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

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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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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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

Turning Points in Physics

Physics of Motion

Dynamics

Physical Quantities And Units

Modern Physics

Engineering 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.