Question

Calculate the rms currents for an ac source is given by v(t) = V0 sinÏt, where V0 = 100V and Ï = 200Ï rad/s when connected across

(a) a 20-μF capacitor,
(b) a 20-mH inductor, and
(c) a 50-Ω resistor.

Answer 1

The rms current can be calculated using the formula Irms = Vrms/Z, where Z represents the impedance. For a capacitor, the impedance is given by Zc = 1/(ωC), for an inductor, the impedance is ZL = ωL, and for a resistor, the impedance is equal to the resistance.

Step-by-step explanation:

The rms current for an AC source can be calculated using the formula Irms = Vrms/Z, where Irms is the rms current, Vrms is the rms voltage, and Z is the impedance.

For a capacitor, the impedance is given by Zc = 1/(ωC), where ω is the angular frequency and C is the capacitance. Plugging in the given values, we have Zc = 1/(200π*20*10^-6) = 0.398 Ω.

For an inductor, the impedance is given by ZL = ωL, where L is the inductance. Plugging in the given values, we have ZL = 200π*20*10^-3 = 25.1 Ω.

For a resistor, the impedance is equal to the resistance, so Z = 50 Ω.