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Module 1: Sinusoidal alternating waveforms

Useful Equations

Average Value: $$V_{dc}=\frac{1}{T}\int_0^T{v(t)dt}=\frac{\text{algebraic sum of areas}}{\text{length of curve}}$$ Using the oscilloscope: $$V_{dc}= (\text{vertical shift in div.})\times (\text{vertical sensitivity in V/div.})$$

Effective Value: $$V_{rms}=\sqrt {\frac{1}{T}area[v(t)^2]}=\sqrt { \frac{1}{T}\int_0^T{v(t)^2dt} }$$ For sinusoidal waveform \(v(t)=V_m sin(\omega t+\theta_v)\): $$ V_{rms} = \frac{ V_m }{ \sqrt{2} } = 0.707V_m$$

Phase Difference: $$ \theta = \frac{ \text{phase shift (no. of div.)} }{ \text{period (no. of div.)} } \times 360^\circ $$