<Dd> I RMS = I p 1 T 2 − T 1 ∫ T 1 T 2 sin 2 ⁡ (ω t) d t . (\ displaystyle I_ (\ text (RMS)) = I_ (\ text (p)) (\ sqrt ((1 \ over (T_ (2) - T_ (1))) (\ int _ (T_ (1)) ^ (T_ (2)) (\ sin ^ (2) (\ omega t)) \, dt))).) </Dd> <P> Using a trigonometric identity to eliminate squaring of trig function: </P> <Dl> <Dd> I RMS = I p 1 T 2 − T 1 ∫ T 1 T 2 1 − cos ⁡ (2 ω t) 2 d t I RMS = I p 1 T 2 − T 1 (t 2 − sin ⁡ (2 ω t) 4 ω) T 1 T 2 (\ displaystyle (\ begin (aligned) I_ (\ text (RMS)) & = I_ (\ text (p)) (\ sqrt ((1 \ over (T_ (2) - T_ (1))) (\ int _ (T_ (1)) ^ (T_ (2)) (1 - \ cos (2 \ omega t) \ over 2) \, dt))) \ \ I_ (\ text (RMS)) & = I_ (\ text (p)) (\ sqrt ((1 \ over (T_ (2) - T_ (1))) \ left ((t \ over 2) - (\ sin (2 \ omega t) \ over 4 \ omega) \ right) _ (T_ (1)) ^ (T_ (2)))) \ end (aligned))) </Dd> </Dl> <Dd> I RMS = I p 1 T 2 − T 1 ∫ T 1 T 2 1 − cos ⁡ (2 ω t) 2 d t I RMS = I p 1 T 2 − T 1 (t 2 − sin ⁡ (2 ω t) 4 ω) T 1 T 2 (\ displaystyle (\ begin (aligned) I_ (\ text (RMS)) & = I_ (\ text (p)) (\ sqrt ((1 \ over (T_ (2) - T_ (1))) (\ int _ (T_ (1)) ^ (T_ (2)) (1 - \ cos (2 \ omega t) \ over 2) \, dt))) \ \ I_ (\ text (RMS)) & = I_ (\ text (p)) (\ sqrt ((1 \ over (T_ (2) - T_ (1))) \ left ((t \ over 2) - (\ sin (2 \ omega t) \ over 4 \ omega) \ right) _ (T_ (1)) ^ (T_ (2)))) \ end (aligned))) </Dd>

Derivation of formula for the rms value of current