Chapter 32: Q. 31 (page 925)

At what frequency f do a $1.0 μ F$ capacitor and a $1.0 μ H$ inductor have the same reactance? What is the value of the reactance at this frequency?

Short Answer

Expert verified

Frequency ; f $= 159 k H z$

Reactance ; $X = 9.98 \times 10^{- 4} Ω$

Step by step solution

:Given Information

We have been given that

Capacitance of capacitor, $(C) = 1.0 μ F = 10^{- 6} F$

Inductance of inductor, $(L) = 1.0 μ H = 10^{- 6} H$

We need to find out the frequency at which the reactance of inductor and capacitor is same and the reactance at that frequency.

Explanation

Given , $C = 1 μ F$ and $L = 1 μ H$

As we know Capacitive Reactance ;

$X_{C} = \frac{1}{2 π f C} . . . . . (1)$

where f is frequency ;

C is capacitance;

$X_{C}$ is capacitive reactance

Also,

Inductive Reactance ; $X_{L} = 2 π f L$ $. . . . . . . (2)$

where f is frequency ;

L is inductance

Since, both Reactance are same $i . e X_{L} = X_{C}$

$\Rightarrow 2 π f L = \frac{1}{2 π f C} \Rightarrow f = \frac{1}{2 π \sqrt{C L}} = \frac{1}{2 (3.14) \sqrt{(1 \times 10^{- 6} F) (1 \times 10^{- 6} H)}} \Rightarrow f = 159 k H z$

Now reactance at frequency ,f

$X_{L} = X_{C} = 2 π f L = 2 (3.14) (159 \times 10^{3} H z) (1 \times 10^{- 6} H) = 9.98 \times 10^{- 4} Ω$

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.

At what frequency f do a $1.0 μ F$ capacitor and a $1.0 μ H$ inductor have the same reactance? What is the value of the reactance at this frequency?

Short Answer

Step by step solution

:Given Information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Work Energy and Power

Torque and Rotational Motion

Radiation

Kinematics Physics

Rotational Dynamics

Energy Physics

Study anywhere. Anytime. Across all devices.

At what frequency f do a 1.0μFcapacitor and a 1.0μHinductor have the same reactance? What is the value of the reactance at this frequency?

Short Answer

Step by step solution

:Given Information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Work Energy and Power

Torque and Rotational Motion

Radiation

Kinematics Physics

Rotational Dynamics

Energy Physics

Study anywhere. Anytime. Across all devices.

At what frequency f do a $1.0 μ F$ capacitor and a $1.0 μ H$ inductor have the same reactance? What is the value of the reactance at this frequency?