Answer

Verified

349.2k+ 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.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference Between Plant Cell and Animal Cell

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Change the following sentences into negative and interrogative class 10 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE