The circuit diagram used to study the characteristic curve of a zener diode is connected to variable power supply (0 $$-$$ 15 V) as shown in figure. A zener diode with maximum potential V_{z} = 10 V and maximum power dissipation of 0.4 W is connected across a potential divider arrangement. The value of resistance R_{P} connected in series with the zener diode to protect it from the damage is ________________ $$\Omega$$.

A potential barrier of 0.4 V exists across a p-n junction. An electron enters the junction from the n-side with a speed of 6.0 $$\times$$ 10^{5} ms^{$$-$$1}. The speed with which electron enters the p side will be $${x \over 3} \times {10^5}$$ ms^{$$-$$1} the value of x is _____________.

(Given mass of electron = 9 $$\times$$ 10^{$$-$$31} kg, charge on electron = 1.6 $$\times$$ 10^{$$-$$19} C.)

A transistor is used in an amplifier circuit in common emitter mode. If the base current changes by 100 $$\mu$$A, it brings a change of 10 mA in collector current. If the load resistance is 2 k$$\Omega$$ and input resistance is 1 k$$\Omega$$, the value of power gain is x $$\times$$ 10^{4}. The value of x is _____________.

A zener of breakdown voltage V_{z} = 8 V and maximum zener current, I_{ZM} = 10 mA is subjectd to an input voltage V_{i} = 10 V with series resistance R = 100 $$\Omega$$. In the given circuit R_{L} represents the variable load resistance. The ratio of maximum and minimum value of R_{L} is _____________.