In a p-n junction diode, the current I can be expressed as
`I=I_(0)"exp"((eV)/(2k_(B)T)-1)`
where `I_(0)` is called the reverse saturation current, V is the voltage across the diode and is positive for forward bias and negative for reverse bias, and I is the current through the diode, `k_(B)` is the Boltzmann constant `(8.6xx10^(-5)eV//K)` and T is the absolute temperature. If for a given diode `I_(0)=5xx10^(-12)`A and T = 300 K, then
(a) What will be the forward current at a forward voltage of 0.6 V ?
(b) What will be the increase in the current if the voltage across the diode is increased to 0.7 V ?
(c ) What is the dynamic resistance?
(d) What will be the current if reverse bias voltage changes from 1 V to 2 V ?

Explanation

Current passing through junction diode,
`I=I_(0)["exp"((eV)/(k_(B)T))-1]`
where `I_(0)=` Reverse saturated current `=5xx10^(-12)A`
`T=300K`
`k_(B)=8.6xx10^(-5)eVK^(-1)`
`=8.6xx10^(-5)xx1.6xx10^(-19)JK^(-1)`
`=13.76xx10^(-24)JK^(-1), 1 eV=1.6xx10^(-19)JK^(-1)`
(a) When V = 0.6 V then
`I=I_(0)["exp"((eV)/(k_(B)T))-1]" "...(1)`
but `(eV)/(k_(B)T)=(1.6xx10^(-19)xx0.6)/(13.76xx10^(-24)xx300)=0.23255xx10^(2)`
`~~23.26`
`therefore` From equation (1),
`I_(1)=I_(0)["exp"(23.26)-1]A`
`=5xx10^(-12)["exp"(23.26)-1]A`
`=5xx10^(-12)[e^(23.26)-1]A`
`=5xx10^(-12)[log(0.4343xx23.26)-1]A`
`=5xx10^(-12)[1.2586xx10^(10)-1]A`
Neglecting 1 compare to `1.2586xx10^(10)`
`=5xx10^(-12)xx1.2586xx10^(10)A`
`therefore I_(1)=0.06293 A`
(b) When V = 0.7V then
From equation (1),
Taking `(eV)/(k_(B)T)=(1.6xx10^(-19)xx0.7)/(13.76xx10^(-24)xx300)=27.13`
`I_(2)=I_(0)["exp"((eV)/(k_(B)T))-1]A`
`=5xx10^(-12)[27.13log(0.4343)-1]A`
`=5xx10^(-12)[6.07xx10^(11)-1]A`
Neglecting 1 compare to `6.07xx10^(11)`
`=5xx10^(-12)xx6.07xx10^(11)A`
`therefore I_(2)=3.035A`
`therefore ` Increase in current `DeltaI=I_(2)-I_(1)`
`=3.0350-0.06293`
`=2.97207A`
`~~2.972`A
(c ) `DeltaV=0.7-0.6=0.1V`
and `DeltaI=2.972A`
`therefore` Dynamic variable resistance,
`r_(d)=(DeltaV)/(DeltaI)=(0.1)/(2.972)=0.03364Omega`
`therefore r_(d)~~0.0336Omega`
(d) When voltage varies from 1 V to 2V then current `I_(0)=5xx10^(-12)`A remains constant it shows that in reverse bias the dynamic resistance is infinite.