An electrical appliance draws an rms current of 10.0 A and has an average power

Question

An electrical appliance draws an rms current of 10.0 A and has an average power of 720 W when connected to a power source with an rms emf of 120 V at 60.0 Hz. (a) What is the impedance of the appliance? The appliance could be analyzed as a series combination of a resistor, capacitor and inductor with the same electrical properties. (b) Considering the appliance in this fashion, what is the value of the series resistance? (c) The quantity XL - XC (as found in the impedance equation) is called the total reactance. What is the magnitude of the total reactance of the appliance? (d) What is the instantaneous power at time t = 0 s?

Explanation / Answer

a) the impedance of the appliance can be found by simply dividing the Vrms by the irms V/I=Z= 12 b) to find the resistance of the resistor we can use Pavg=irms2(R) R=P/i2 R=7.2 c) to find the total reactance we can say Z=(R2 + (XL-XC)2 (XL-XC)=(Z2-R2) (XL-XC)= 9.6 d)for instantaneous power we must use amplitudes and the complete expression for i in a a RLC AC circuit P=i2R P=(irms*2*sin(t-))2(R) P=(i2 sin(0-))2 *(R) where =tan-1( (XL-XC)/(R)) =53.13 degrees so when we plug it in to the Power equation we made we find P=(i2 sin)2 *(R) (XL-XC)= 9.6 d)for instantaneous power we must use amplitudes and the complete expression for i in a a RLC AC circuit P=i2R P=(irms*2*sin(t-))2(R) P=(i2 sin(0-))2 *(R) where =tan-1( (XL-XC)/(R)) =53.13 degrees so when we plug it in to the Power equation we made we find P=921.6 W

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.