Explanation
If the resistivity of an alloy is $$\rho '$$ and that of constituent metal is $$\rho $$ then :
Form factor of half wave rectifier is $$=\dfrac{{{I}_{rms}}}{{{I}_{av}}}.....(1)$$
RMS value of current is
$$ {{I}_{rms}}=\sqrt{\dfrac{1}{2\pi }\int\limits_{0}^{\pi }{{{i}^{2}}d\theta }} $$
$$ =\sqrt{\dfrac{1}{2\pi }\int\limits_{0}^{\pi }{I_{\max }^{\pi }{{\sin }^{2}}\theta d\theta }} $$
$$ =\dfrac{{{I}_{\max }}}{\sqrt{2\pi }}\sqrt{\dfrac{1}{2\pi }\int\limits_{0}^{\pi }{{{\sin }^{2}}\theta d\theta }} $$
$$ =\dfrac{{{I}_{\max }}}{\sqrt{4\pi }}\sqrt{\left[ \theta -\dfrac{1}{2}\sin 2\theta \right]}_{0}^{\pi } $$
$$ =\dfrac{{{I}_{\max }}}{\sqrt{4\pi }}\sqrt{\pi } $$
$$ =\dfrac{{{I}_{\max }}}{2} $$
Average value of current,
$$ {{I}_{av}}=\dfrac{1}{2\pi }\int\limits_{0}^{\pi }{id\theta } $$
$$ =\dfrac{1}{2\pi }\int\limits_{0}^{\pi }{{{I}_{\max }}\sin \theta d\theta } $$
$$ =\dfrac{{{I}_{\max }}}{\pi } $$
So, put above values in equations (1) and (2)
Form factor,
$$ =\dfrac{\dfrac{{{I}_{\max }}}{2}}{\dfrac{{{I}_{\max }}}{\pi }} $$
$$ =\dfrac{\pi }{2} $$
$$ =1.57 $$
When a diode is connected across AC source, it works as both half and full wave rectifier. Because for positive half of cycle it allows the current to flow but for negative half of cycle it stops current to flow.
The value of reverse voltage at which this occurs is controlled by the amount ot doping of the diode. A heavily doped diode has a low Zener breakdown voltage, while a lightly doped diode has a high Zener breakdown voltage. At voltages above approximately 8V, the predominant mechanism is the avalanche breakdown.
Light emitting diode is a forward biased P-N junction which emits light.
The voltage across it = 2 v
Battery voltage = 6 v
Hence total voltage in the circuit = V = 6 - 2 = 4 v
since a LED has 0 resistance in the forward biased region, total resistance in the circuit
= 0 + r = r
current I = 10 mA = 10/1000 A = 0.01 A
we know that,
R = V/I
=> r = 4/0.01 = 400Ω
Hence the value of the limiting resistor is 400Ω
Semiconductor mobility depends on the impurity concentrations including donor and acceptor concentrations, defect concentration, temperature, and electron and hole concentrations. Mobility describes the relation between drift velocity of electrons or holes and an applied electric field in a solid.
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