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Answer :
Final answer:
Therefore the correct option is B. The wattless component of the rms current in the circuit is 0.5 ampere.
Explanation:
According to the given information, the coil has an inductance of 2.2H/π and is joined in series with a resistance of 220 ohms. When an alternating e.m.f. of 220 V at 50 c.p.s. is applied to it, we need to find the wattless component of the rms current in the circuit.
For an inductor, the reactance (X) is given by X = 2πfL, where f is the frequency of the AC source and L is the inductance of the coil. The reactance of the inductor is purely imaginary and represents the wattless component of the current. In this case, the frequency is 50 Hz, so the reactance is X = 2π * 50 * (2.2H/π) = 220Ω.
Since the coil is in series with a resistance of 220 ohms, the total impedance of the circuit is the sum of the resistance and reactance: Z = R + X = 220 + 220 = 440Ω.
According to Ohm's law, the rms current in the circuit can be calculated using the formula I = Vrms / Z, where Vrms is the rms voltage and Z is the impedance. Plugging in the values, we get I = 220V / 440Ω = 0.5A.
Therefore, the wattless component of the rms current in the circuit is 0.5 ampere (B).
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