प्रत्यावर्ती धारा `I=I_(1)cosomegat+I_(2)sinomegat` के लिए वर्ग माध्य मूल धारा का मान ज्ञात कीजिए

Explanation

`:.` वर्ग माध्य मूल धारा
`I_(rms)=sqrt(bar((I^(2))))`
`:'I=I_(1)cosomegat+I_(2)sinomegat`
`:.I^(2)=(I_(1)cosomegat+I_(2)sinomegat)^(2)`
`I^(2)=I_(1)^(2)cos^(2)omegat+I_(2)^(2)sin^(2)omegat+2I_(1)I_(2)sinomegatcosomegat`
एक पूर्ण चक्र में औसत मान
`bar((I^(2)))=(int_(0)^(T)I_(2)dt)/(T)`
`=(1)/(T)[int_(0)^(T)I_(1)^(2)cos^(2)omegatdt+int_(0)^(T)I_(2)^(2)sin^(2)omegatdtint_(0)^(T)I_(1)I_(2)sin2omegatdt]`
`:'2sinomegatcosomegat=sin2omegat`
अब `int_(0)^(T)cos^(2)omegatdt=(T)/(2)`
`int_(0)^(T)sin^(2)omegatdt=(T)/(2)`
`int_(0)^(T)sin2omegat=0`
`bar((I_(2)))=(1)/(T)[I_(1)^(2)xx(T)/(2)+I_(2)^(2)xx(T)/(2)+I_(1)I_(2)xx0]`
`=(I_(1)^(2)+I_(2)^(2))/(2)`
`:.I_(rms)=sqrt((I_(1)^(2)+I_(2)^(2))/(2))=(1)/(sqrt2)(I_(1)^(2)+I_(2)^(2))^(1//2)`