The rms value of an ac current of 50 Hz is 10 amp. The time taken by the alternating current in

step 1 In this problem I can write the value of IRMS is equal to i0 by root 2. Solving it further I can

The rms value of an ac current of 50 Hz is 10 amp. The time...

The rms value of an ac current of $50 \mathrm{~Hz}$ is 10 amp. The time taken by the alternating current in reaching from zero to maximum value and the peak value of current will be, (a) $2 \times 10^{-2}$ sec and $14.14 \mathrm{amp}$ (b) $1 \times 10^{-2}$ sec and $7.07 \mathrm{amp}$ (c) $5 \times 10^{-3}$ sec and $7.07$ amp (d) $5 \times 10^{-3} \mathrm{sec}$ and $14.14 \mathrm{amp}$

The rms value of an ac current of $50 \mathrm{~Hz}$ is 10 amp. The time taken by the alternating current in reaching from zero to maximum value and the peak value of current will be,
(a) $2 \times 10^{-2}$ sec and $14.14 \mathrm{amp}$
(b) $1 \times 10^{-2}$ sec and $7.07 \mathrm{amp}$
(c) $5 \times 10^{-3}$ sec and $7.07$ amp
(d) $5 \times 10^{-3} \mathrm{sec}$ and $14.14 \mathrm{amp}$

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Key Concepts

RMS and Peak Value Relationship

In AC circuits, the root mean square (RMS) value of a sinusoidal signal represents the equivalent DC value that would deliver the same power. The peak value, which is the maximum instantaneous value of the sinusoid, is obtained by multiplying the RMS value by the square root of 2. This relationship is fundamental for converting between the effective and the maximum values of AC currents or voltages.

Frequency and Period

Frequency is defined as the number of complete cycles of a waveform that occur per second, and is measured in hertz (Hz). The period is the time taken for one complete cycle, and can be calculated as the reciprocal of the frequency. This concept is important for analyzing the time domain characteristics of periodic signals.

Sine Wave Phase Relationships

For a sinusoidal waveform that starts at zero, the maximum (peak) value is reached at a quarter of the period due to the inherent properties of the sine function. This phase relationship is crucial when determining the time it takes for a sine wave to go from zero to its peak value, as it directly ties the time interval to the overall period of the wave.

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