What is the role of cosφ in calculating power in LRC series circuits?

[waley]

Homework Statement

With just about any problem asking for "rate at which source is delivering electrical energy to the circuit" or "find the power of the circuit" in a LRC circuit, I get that you have to calculate for the average power. But the multiple equations confuse me - sometimes in problems like I mentioned above, you'd use P=0.5IVcosφ and sometimes you do without the cosφ term. If the circuit were at resonance, or in other words the power factor was raised to unity, then I see how cosφ disappears, but when you're talking about the entire circuit will all L, R, C components, not at resonance, why is it that I sometimes see people doing the problem without the cosφ?

Homework Equations

The Attempt at a Solution

 

[cnh1995]

why is it that I sometimes see people doing the problem without the cosφ?

It's because they are finding the apparent power and not the active (or real) power.
Look these terms up and post if anything is unclear.

 

[Diegor]

The instant power delivered by the source to the rest of the circuit is iv being i and v the instant current and instant voltage If you consider that i and v are sin functions and you do the product you will find the three expressions for power related to an AC voltage source. Active power, apparent power and reactive power each one with a different meaning. In this powers the formula may change if the voltage and currents used are the amplitudes or the rms values. You should post your attempt of solving a circuit so we can help in the specific case.