يغذي تيار متناوب يعطى توتره اللحظي بالعلاقة:

U=120√2cos100πt

Ueff = 120 V

ω = 100π rad/s

m = 1 kg

∆t = 72ºC

∆t' = 420 s

Pavg = 600 watt

cosφ = 1/2

Q = E

m.C0.∆t = Pavg.∆t'

m.C0.∆t = Ueff.Ieff.φ1.∆t'

φ1 = 0

cosφ1 = 1

Ieff = (m.C0.∆t) / (Ueff.∆t')

Ieff = (1*4200*72) / (120*420) = 6 A

Pavg = Ueff.Ieff.cosφ2

Ieff2 = Pavg / Ueff.cosφ2

Ieff2 = 600 / 120*1/2 = 10 A

i1 = Imax.cos(ωt-φ1) 

Imax = Ieff

i1 = 6√2*cos(100πt+0) 

i1 = 6√2*cos(100πt)

i2 = Imax.cos(ωt-φ2)

Imax = Ieff.√2 = 10√2 A

ω = 100π rad/s

cosφ2 = 1/2

φ2 = ±π/3 rad

φ2 = π/3 rad

i2 = 10√2.cos(100πt-π/3)

Ieff = Ieff1 + Ieff2

لأن التيار متأخر بالطور عن التوتر.

نربع طرفي العلاقة الشعاعية فنجد:

I2eff = I2eff1 + I2eff2 + 2Ieff1.Ieff2.cos(φ2-φ1)

I2eff = 36 + 100 + 2(6)(10)(1/2) = 196

Ieff = 14 A

cosφ = (Ieff1 + I'eff) / Ieff

cosφ = (Ieff1 + Ieffφ2) / Ieff

cosφ = 6+5/14 = 11/14

Pavg = Pavg1 + Pavg2

Pavg = Ueff.Ieff1.cosφ1 + Pavg2

= 120*6*1 + Pavg2

= 720 + 600 = 1320 watt

Pavg = Ueff.Ieff.cosφ

cosφ = Pavg / Ueff.Ieff

cosφ = 1320/120*14 = 11/14

φ = π/3 rad

Ieff = Ieff1 + Ieff2 + Ieff3

Ieff3 = ω.c.Ueff

Ieff = Ueff / Xc

Ieff3 = Ieff2.sinφ2

Ieff3 = 10*(√3/2) = 5√3 A

C = Ieff3/ω.Ueff

C = 5√3 / 100π*120

C = √3 / 2400π F

Ieff = Ieff1 + I'eff = Ieff1 + Ieff2.cosφ2

Ieff = 6 + 10(1/2) = 11 A