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A saw-tooth voltage waveform has a peak value V0. If the rms voltage over a complete cycle is expressed as V_rms = 2*V0 / sqrt(6*N), find the value of N.

1. 1
2. 2
3. 3
4. 6

Correct answer: 2

Solution

For a sawtooth wave that varies linearly from -V0 to +V0 over period T: V²_rms = (1/T) * integral from 0 to T of V0²*(2t/T - 1)² dt = V0²/3. So V_rms = V0/sqrt(3). Setting equal to 2*V0/sqrt(6*N): V0/sqrt(3) = 2*V0/sqrt(6*N) → sqrt(6*N) = 2*sqrt(3) → 6*N = 12 → N = 2.

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