Answer
Verified
378k+ views
Hint: In contrast to direct current (DC), which flows only in one direction, alternating current (AC) is an electric current that regularly reverses direction and changes its magnitude continuously over time.
Complete step by step answer:
In an AC circuit, resonance is described as the state in which the circuit's inductive reactance equals its capacitive reactance. Resonance frequency is the value of angular frequency of alternating emf (or potential difference across the power source) for which resonance is formed in the circuit.
\[P = IV\], where I is the current through the element and \[V\] is the voltage across it, determines whether a circuit element dissipates or produces electricity. Since the current and voltage in an ac circuit are both time dependent, the instantaneous power \[p\left( t \right) = i\left( t \right)v\left( t \right)\] is also time dependent.
Now, coming to the question, Power dissipated in an AC circuit,
$P = IV\cos \phi $ [$\cos \phi $ is power factor; $\phi $ is phase difference]
\[V = 230\sin \left( {\omega t + \dfrac{\pi }{2}} \right)\]____(i)
$I = 20\sin \left( {\omega t} \right)$_____(ii)
From equation (i) we get peak value ${V_0} = 230\,V$ and phase angle $\theta = \dfrac{\pi }{2}$
From equation (ii) we get peak current ${I_0} = 20\,A$
Power dissipated $P = IV\cos \phi $
$\Rightarrow P = \dfrac{{{V_0}}}{{\sqrt 2 }} \times \dfrac{{{I_0}}}{{\sqrt 2 }}\cos \left( {\dfrac{\pi }{2}} \right)$
$\Rightarrow P = \dfrac{{230}}{{\sqrt 2 }} \times \dfrac{{20}}{{\sqrt 2 }} \times \left( 0 \right)$ $[\because \cos \dfrac{\pi }{2} = 0]$
$\therefore P = 0$
Therefore, power dissipated through the AC circuit is zero.
Note:Peak power dissipation is also normally only relevant in specific applications since peak power is an instantaneous value that occurs only when the voltage and current are at their highest levels. The \[rms\] power is the most important power specification in an AC circuit.
Complete step by step answer:
In an AC circuit, resonance is described as the state in which the circuit's inductive reactance equals its capacitive reactance. Resonance frequency is the value of angular frequency of alternating emf (or potential difference across the power source) for which resonance is formed in the circuit.
\[P = IV\], where I is the current through the element and \[V\] is the voltage across it, determines whether a circuit element dissipates or produces electricity. Since the current and voltage in an ac circuit are both time dependent, the instantaneous power \[p\left( t \right) = i\left( t \right)v\left( t \right)\] is also time dependent.
Now, coming to the question, Power dissipated in an AC circuit,
$P = IV\cos \phi $ [$\cos \phi $ is power factor; $\phi $ is phase difference]
\[V = 230\sin \left( {\omega t + \dfrac{\pi }{2}} \right)\]____(i)
$I = 20\sin \left( {\omega t} \right)$_____(ii)
From equation (i) we get peak value ${V_0} = 230\,V$ and phase angle $\theta = \dfrac{\pi }{2}$
From equation (ii) we get peak current ${I_0} = 20\,A$
Power dissipated $P = IV\cos \phi $
$\Rightarrow P = \dfrac{{{V_0}}}{{\sqrt 2 }} \times \dfrac{{{I_0}}}{{\sqrt 2 }}\cos \left( {\dfrac{\pi }{2}} \right)$
$\Rightarrow P = \dfrac{{230}}{{\sqrt 2 }} \times \dfrac{{20}}{{\sqrt 2 }} \times \left( 0 \right)$ $[\because \cos \dfrac{\pi }{2} = 0]$
$\therefore P = 0$
Therefore, power dissipated through the AC circuit is zero.
Note:Peak power dissipation is also normally only relevant in specific applications since peak power is an instantaneous value that occurs only when the voltage and current are at their highest levels. The \[rms\] power is the most important power specification in an AC circuit.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE