Determine the average and effective values of the given waveform.

Concept:

RMS Value: The RMS or effective value of an alternating current or voltage is given by that steady current or voltage which when flows or applied to a given resistance for a given time produces the same amount of heat as when the alternating current or voltage is flowing or applied to the same resistance for the same time.

\({V_{RMS}} = \sqrt {\frac{1}{T}\;\mathop \smallint \limits_{t = 0}^T {V^2}\;dt\;\;\;\;\;} \;\;\;\;\;\;\;\)

Average Value: The average value or mean value of an alternating current is expressed by that steady current that transfers across any circuit the same charge as is transferred by that alternating current during the same time.

\({V_{Avg}} = \frac{1}{T}\mathop \smallint \limits_{t = 0}^{t = T} {V_0}\;dt\)

Calculation:

RMS Value = \({V_{RMS}} = \sqrt {\frac{1}{T}\;\mathop \smallint \limits_{t = 0}^T {V^2}\;dt\;\;\;\;\;} \;\;\;\;\;\;\;\)

\({V_{RMS}} = \sqrt {\frac{1}{{0.3}}\mathop \smallint \limits_{t = 0}^{t = 0.1} {{20}^2}.dt} \)

\({V_{RMS}} = \sqrt {\frac{{400}}{{0.3}}} \left[ {0.1 - 0} \right]\)

\({V_{RMS}} = \sqrt {\frac{{400}}{{0.3}}} \times 0.1\)

\({V_{RMS}} = \sqrt {133.3} \) V

Average Value = \({V_{Avg}} = \frac{1}{T}\mathop \smallint \limits_{t = 0}^{t = T} {V_0}\;dt\)

\({V_{Avg}} = \frac{1}{{0.3}}\mathop \smallint \limits_{t = 0}^{t = 0.1} 20\;dt\)

\({V_{Avg}} = \frac{{20}}{{0.3}}\left[ {0.1 - 0} \right]\)

\({V_{Avg}} = \frac{{20}}{3}\)

V_Avg  =  6.67 V