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    the rms value of an ac sinusoidal current is 10a. its peak value is

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    The rms value of current in an AC circuit is 10A . What is the peak current?

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    Question

    The rms value of current in an AC circuit is 10A. What is the peak current?

    A

    14.1A

    B

    35.2A

    C

    58.9A

    D

    23.5A

    Easy Open in App Solution Verified by Toppr

    Correct option is A)

    Answer:− A

    Relation between peak current and rms current is:

    I rms ​ = 2 ​ I 0 ​ ​ V 0 ​ = 2 ​ ×10=14.1A

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    The rms value of current in an ac circuit is 10A. What is the peak current ?

    Using the formula I("rms")=(I(0))/(sqrt(2)) The prak value of current I(0)=sqrt(2)xx I("rms") = sqrt(2)xx10 =1.414xx10 I(0)=14.14 A

    Home English Class 12 Physics Chapter Alternating Current

    The rms value of current in an...

    The rms value of current in an ac circuit is 10A. What is the peak current ?

    Answer

    Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

    Updated On: 12-03-2022

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    Text Solution Solution Using the formula I rms = I 0 2 – √ Irms=I02

    The prak value of current

    I 0 = 2 – √ × I rms I0=2×Irms = 2 – √ ×10=1.414×10 =2×10=1.414×10 I 0 =14.14A I0=14.14A

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    Very Important Questions

    यदि द्विआधारी संक्रिया धनात्मक पूर्णांक समुच्चय

    Z + Z+

    में इस प्रकार परिभाषिता है कि

    a∗b= 2 ab ∀a,b∈ Z + a∗b=2ab∀a,b∈Z+ तो संक्रिया *, Z + Z+

    में किस नियम का पालन करती है।

    f(x) = 2x + 3 द्वारा प्रदत्त फलन

    f:R→R f:R→R

    पर विचार कीजिए कि f व्युत्क्रमणीय है। f का प्रतिलोम फलन भी ज्ञात कीजिए।

    दर्शाइए कि एक द्विआधारी संक्रिया जो

    A=R−{−1} A=R-{-1} पर सभी a,b∈A a,b∈A

    के लिए a*b = a + b + ab द्वारा परिभाषित है। क्रम-विनिमेय तथा साहचर्य है। A में * का तत्समक अवयव ज्ञात कीजिए तथा सिद्ध कीजिए कि A का प्रत्येक अवयव व्युत्क्रमणीय है |

    यदि f,g:R→R f,g:R→R

    फलन इस प्रकार परिभाषित है कि

    f(x)= x 2 +1,g(x)=2x−3 f(x)=x2+1,g(x)=2x-3

    तो gof (x) ज्ञात कीजिए।

    यदि f,g:R→R f,g:R→R

    फलन इस प्रकार परिभाषित है कि

    f(x)= x 2 +1,g(x)=2x−3 f(x)=x2+1,g(x)=2x-3

    तो gog(3) ज्ञात कीजिए।

    धनात्मक परिमेय संख्याओं के समुच्चय

    Q + Q+

    में निम्नलिखित प्रकार से परिभाषित एक द्विआधारी संक्रिया है, तो

    a∗b= ab 4 a∗b=ab4

    सिद्ध करो कि * क्रम-विनिमय तथा साहचर्य है।

    Q + Q+

    में * का प्रतिलोम अवयव यदि कोई हो, तो ज्ञात कीजिए।

    FAQs on Alternating Current

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    The RMS value of current in an AC circuit is 10 A What class 12 physics CBSE

    The RMS value of current in an AC circuit is 10 A What is the peak current A 141A B 352A C 589A D 235A

    The RMS value of current in an AC circuit is 10 A. What is the peak current?

    A. 14.1A B. 35.2A C. 58.9A D. 23.5A Verified 129.6k+ views

    Hint: We have already learnt the derivation for relation between peak value of AC and RMS value of AC in chapter Alternating Current of unit 4 in Class 12. Since, we have already given the RMS value of current. Simply, substitute the numerical values given in below given mathematical formula for finding the asked value.Complete step by step answer:

    Given that, the RMS value of current in an AC circuit is 10 A.Now, RMS value i.e., Root Mean Square value which is also known as Effective value of Alternating Current or Virtual value of Alternating Current. We may define it as that value of steady Current (or Direct Current) which would generate the same amount of heat as it generated by alternating Current in the same circuit for the full time period.

    In simple words, we can say that the amount of heat produced due to alternating current in a circuit A then the same amount of heat should be produced in an another circuit B due to Direct current and that value of direct current is known as the Root Mean Square value of Alternating current. It is represented as

    I ν Iν or I effective Ieffective or I RMS IRMS

    .Through derivation, we concluded with the mathematical expression as:

    I RMS = I 0 2 – √ IRMS=I02

    ……………………………………… Eq.1

    Where, I 0 I0

    = peak current or maximum current.

    I RMS IRMS

    = Root Mean Square value of Alternating current.

    Substituting value of

    1 2 – √ =0.7071 12=0.7071

    in above formula, we get

    I RMS =0.707 I 0 IRMS=0.707I0 ……………………………. Eq.2

    We need to find the value of peak current. Peak current is also called maximum current.

    Substitute the numerical value of

    I RMS IRMS

    from the question into either Eq.1 or Eq.2,

    10=0.707 I 0 ⇒ 10 0.707 = I 0 ⇒14.144= I 0

    10=0.707I0⇒100.707=I0⇒14.144=I0

    ∴ I 0 =14.144 ∴I0=14.144 approx. I 0 =14.1 I0=14.1 A

    The peak value of alternating current is 14.1 Ampere in a circuit where RMS value of current is 10 Ampere.

    So, option A is correct.Note: Always write the units of physical quantity in the end of solution. RMS value for any physical quantity can never be negative. Also, in RMS value we considered the full cycle of alternating current instead of half cycle which we consider in Average value of AC.Go through from the derivation for more clarity.

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