Answer :
Final answer:
The average emf during a positive half cycle of a 220 V RMS AC supply is approximately 155.5 V, which is half the peak voltage of the sinusoidal wave. None of the provided answer options match, so clarification or additional information is needed. So, the correct answer is None of the above.
Explanation:
The question asks for the average electromotive force (emf) during a positive half cycle of an alternating current (AC) supply given to be 220 V, which we understand to be the root mean square (RMS) voltage. To find the average emf over a half cycle for a sinusoidal source, we integrate the voltage function V(t) = V0 sin(ωt) over a half cycle and divide by the time period of the half cycle.
For a sinusoidal AC source, the RMS voltage, VRMS, is related to the peak voltage, V0, by V0 = VRMS √2. Therefore, the peak voltage for a 220 V RMS supply is 220 V √2, approximately 311 V. This peak value occurs once every half cycle, meaning the positive peak will be 311 V and the negative peak will be -311 V.
However, the average of these peaks over a half cycle will be half the peak voltage due to the symmetrical nature of the sine wave. Hence, the average emf during the positive half cycle will be 0.5 x 311 V ≈ 155.5 V. Since no provided answer options exactly match this result, we must clarify the question or provide additional information to our student.