The beam width-between-first-null of a uniform linear array of N equally-spaced (element spacing = d) equally-excited antennas is determined by

Elements of a linear array of three equally spaced (element spacing $$0.5\lambda $$ ) vertical mast radiators are excited as given in Fig. For the horizontal plane radiation pattern of the array determine the direction of the major lobe (main lobe or principal lobe) and calculate its half-power-beam-width in degrees.

A semiconductor is irradiated with light such that carriers are uniformly generated throughout its volume. The semiconductor is n-type with $$N_D=10^{19}/cm^3$$. If the excess electron concentration in the steady state id $$\triangle n=10^{15}/cm^3$$ and if $$\tau_p=10\;\mu\;sec$$ [minority carrier life time] the generation rate due to irradiation

The 6 V Zener diode shown in figure has zero Zener resistance and a knee current of 5 mA. The minimum value of R, so that the voltage across it does not fall below 6 V is: