$${q_1},\,{q_2},{q_3},.......{q_m}$$ are $$n$$-dimensional vectors with $$m < n.$$ This set of vectors is linearly dependent. $$Q$$ is the matrix with $${q_1},\,{q_2},{q_3},.......{q_m}$$ as the columns. The rank of $$Q$$ is

In the circuit of adjacent figure the diode connects the $$ac$$ source to pure inductance $$L.$$

The diode conducts for

A single - phase inverter is operated in $$PWM$$ mode generating a single - pulse of width $$2d$$ in the center of each half cycle as shown in figure. It is found that the output voltage is free from $${5^{th}}$$ harmonic for pulse width $${144^0}.$$ What will be percentage of $${3^{rd}}$$ harmonic present in the output voltage $$\,\left( {{V_{03}}/{V_{01\,\,\,\max }}} \right)?$$

A single - phase voltage source inverter is controlled in a single pulse - width modulated mode with a pulse width of $${150^0}$$ in each half cycle. Total harmonic distortion is defined as
$$THD = {{\sqrt {V_{rms}^2 - V_1^2} } \over {{V_1}}} \times 100,\,\,\,$$ Where $${{V_1}}$$ is the $$rms$$ value of the fundamental component of the voltage. The $$THD$$ of output $$ac$$ voltage waveform is