Answer
362.1k+ views
Hint: To answer this question, we first need to understand what is a capacitor. A capacitor (also called a condenser) is a two-terminal passive electrical component that stores energy electrostatically in an electric field. Practical capacitors come in a variety of shapes and sizes, but they all have at least two electrical conductors (plates) separated by a dielectric (i.e., insulator).
Complete step by step answer:
As given in the equation, R=10 ohm, $\cos \Phi = 0.5$(power factor), ${V_{rms}}$= 80V, $f = 50Hz$.As we know that
$\cos \Phi = \dfrac{R}{Z}$
(Here $R$ is the resistance and $Z$ is the impedance)
Substituting values
$0.5 = \dfrac{{10}}{Z}$ so, Z = 20
As we know that $Z = \sqrt {{R^2} + X_C^2} $(where R is the resistance and ${X_c}$is the capacitive impedance)
Putting values of Z and R,
$20 = \sqrt {100 + X_C^2} $
We get ${X_C} = 10\sqrt 3 $
And we know that ${X_C} = \dfrac{1}{{wc}}$
Substituting value of ${X_C}$ and value of $w = 2\pi f$
$10\sqrt 3 = \dfrac{1}{{2 \times 3.14 \times 50 \times C}}$
$\Rightarrow C = \dfrac{1}{{2 \times 50 \times 3.14 \times 10\sqrt 3 }}$
$\Rightarrow C = \dfrac{1}{{100 \times 3.14 \times 10 \times 1.732}}$(putting value of $\sqrt 3 $= 1.732)
$\therefore C = \dfrac{1}{{1000 \times 3.14 \times 1.732}}$
On further calculating we get $C = 9.2 \times {10^{ - 5}}F$
So, the final answer is $C = 9.2 \times {10^{ - 5}}\,F$.
Note: Impedance is the active resistance of an electrical circuit or component to AC current, which is determined by the interaction of reactance and ohmic resistance. In other words, impedance in AC circuits is simply an extension of resistance concepts. We also describe it as any obstruction or measurement of an electric current's resistance to energy flow when voltage is applied.
Complete step by step answer:
As given in the equation, R=10 ohm, $\cos \Phi = 0.5$(power factor), ${V_{rms}}$= 80V, $f = 50Hz$.As we know that
$\cos \Phi = \dfrac{R}{Z}$
(Here $R$ is the resistance and $Z$ is the impedance)
Substituting values
$0.5 = \dfrac{{10}}{Z}$ so, Z = 20
As we know that $Z = \sqrt {{R^2} + X_C^2} $(where R is the resistance and ${X_c}$is the capacitive impedance)
Putting values of Z and R,
$20 = \sqrt {100 + X_C^2} $
We get ${X_C} = 10\sqrt 3 $
And we know that ${X_C} = \dfrac{1}{{wc}}$
Substituting value of ${X_C}$ and value of $w = 2\pi f$
$10\sqrt 3 = \dfrac{1}{{2 \times 3.14 \times 50 \times C}}$
$\Rightarrow C = \dfrac{1}{{2 \times 50 \times 3.14 \times 10\sqrt 3 }}$
$\Rightarrow C = \dfrac{1}{{100 \times 3.14 \times 10 \times 1.732}}$(putting value of $\sqrt 3 $= 1.732)
$\therefore C = \dfrac{1}{{1000 \times 3.14 \times 1.732}}$
On further calculating we get $C = 9.2 \times {10^{ - 5}}F$
So, the final answer is $C = 9.2 \times {10^{ - 5}}\,F$.
Note: Impedance is the active resistance of an electrical circuit or component to AC current, which is determined by the interaction of reactance and ohmic resistance. In other words, impedance in AC circuits is simply an extension of resistance concepts. We also describe it as any obstruction or measurement of an electric current's resistance to energy flow when voltage is applied.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)