An AC current is given by I=I1sinωt+I2cosωt. A hot wire ammeter will give a reading:
I12+I222
I1+I222
I1+I22
I12−I222
Hot wire ammeter read =rms value of current Given AC I=I1sinωt+I2cosωt ⇒I2=I12sin2ωt+I22cos2ωt +2I1I2sinωtcosωt⇒<I2>=I12<sin2ωt>+I22<cos2ωt> +I1I2<sin2ωt>⇒<I2>=I122+I222 + 0 ⇒Irms=<I2>=I12+I222