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Answer :
Final answer:
Calculating the inductive reactance (X_L) using the given frequency and inductance, the reactive component of the current (I_wattless) is found by dividing the applied voltage by X_L, resulting in 2 A, which does not match the provided options.
Explanation:
The question involves calculating the wattless (reactive) component of the rms current in an electrical circuit consisting of a coil and resistance in series, subjected to an alternating e.m.f. To solve this, we need to find the inductive reactance (XL) of the coil and then use it to calculate the reactive component of the current.
The inductive reactance (XL) is given by 2πfL, where f is the frequency in hertz, and L is the inductance in henrys. Using the given values, the inductance L is 2.2H/π, and with a frequency f of 50 c.p.s (or Hz), the inductive reactance XL is:
XL = 2π(50)(2.2/π) = 110 Ω
Since the circuit current leads the applied voltage in a purely inductive circuit, the reactive component of the current can be calculated by dividing the applied voltage by the inductive reactance. Hence:
Iwattless = V / XL = 220 / 110 = 2 A
Therefore, none of the given options (A, B, C, D) match the calculated result of 2 A.
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