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An a.c. current I= i1 sin omegat + i2 si...

An a.c. current I= `i_1 sin omegat + i_2 sin omegat`. The r.m.s. value of the current will be—

A

`(i_1+i_2)//sqrt2`

B

`sqrt({(i_1^2+i_2^2)//sqrt2})`

C

`(i_1+i_2)/sqrt2`

D

`sqrt{((i_1^2+i_2^2))/2}`

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A series combination of an inductor of self-inductance L, capacitor of capacitance C and resistor R is connected to an alternating voltage source of V=V_0sinomegat . The current through the circuit is I=I_0sin(omegat-theta) ,where I_0=V_0/(sqrt(R^2+(omega-1/(omegaC))^2)) and theta=tan^-1 ""1/R(omegaL-1/(omegaC)) . Now that, the frequency of both voltage and current is f=omega/(2pi) . The rms value of these parameters during one complete cycles are V_(rms)=V_0/sqrt2 and I_(rms)=I_0/sqrt2 respectively. These values are shown in alternating voltmeter and ammeter. The power consumed by the circuit P=VI. The mean value i.e., the effective power of the circuit in a complete cycle is overlineP=V_(rms)I_(rms)costheta . This costheta is termed the power factor. the power factor of the circuit is question (i) is

A series combination of an inductor of self-inductance L, capacitor of capacitance C and resistor R is connected to an alternating voltage source of V=V_0sinomegat . The current through the circuit is I=I_0sin(omegat-theta) ,where I_0=V_0/(sqrt(R^2+(omega-1/(omegaC))^2)) and theta=tan^-1 ""1/R(omegaL-1/(omegaC)) . Now that, the frequency of both voltage and current is f=omega/(2pi) . The rms value of these parameters during one complete cycles are V_(rms)=V_0/sqrt2 and I_(rms)=I_0/sqrt2 respectively. These values are shown in alternating voltmeter and ammeter. The power consumed by the circuit P=VI. The mean value i.e., the effective power of the circuit in a complete cycle is overlineP=V_(rms)I_(rms)costheta . This costheta is termed the power factor. The power factor of the circuit in question (iii) is

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