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

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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.