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

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

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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

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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

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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?