Electro Magnetic Induction And Alternating Currents Question 157

Question: If a direct current of value ampere is superimposed on an alternative current I=b,sin,ωt flowing through a wire, what is the effective value of the resulting current in the circuit?

Options:

A) [a212b2]1/2

B) [a2+b2]1/2

C) [a22+b2]1/2

D) [a2+b22]1/2

Show Answer

Answer:

Correct Answer: D

Solution:

  • as current any instant in the circuit will be

    I=Idc+Iac=a+b,sin,ωt

    so, Ieff=[0TI2dt0Tdt]1/2=[1T0T(a+b,sin,ωt)2dt]1/2 i.e.

    Ieff=[1T0T(a2+2ab,sin,ωt+b2,sin2ωt)dt]1/2

    But as 1T0Tsin,ωt,dt=0 and 1T0Tsin2,ωt,dt=12 So, Ieff=[a2+12b2]1/2



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