[" प्र.13प्रत्यावर्ती Prove that for the circuit - "],[P_(av)=V_(rms)I_(rms)cos O/]

Prove that average power consumed in an ac circuit is P_(av) =I_(mns)* V_(mns) * cos theta .

The product e_(rms)I_(rms) is called as

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

Arrange in increasing order to U_(av) U_(mp) and U_(rms) .

Show that the average power transferred to an a.c. circuit is in general given by P= V_(r.m.s) I _(r.m.s) R//Z . Where R is the resistance in the circuit.

Ratio of V_(rms) to V_(averag e) of O :

In an A.C. circuit, i_(rms) and i_(0) are related as