In a `p-n` junction diode, the currect `I` can 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 `(8.6 xx 10^(-5) eV//K)` and `T` is the absolute temperature. If for a given diode `I_(o) = 5 xx 10^(-12) A` and `T = 300 K`, then
(a) What will be the forward current at a formward voltage of `0.6V` ?
(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 current if reverse bias voltage changes from `1 V` to `2 V` ?

Explanation

Here, `I_(0)=5xx10^(-12)A, T=300K, k_(B) =8.6xx10^(-5)eVK^(-1)=8.6xx10^(-5)xx1.6xx10^(-19)JK_(-1)`
If `V=0.6V`, then`(eV)/(k_T)=(1.6xx10^(-19)xx0.6)/(8.6xx10^(-5)xx1.6xx10^(-19)xx300)=23.26`
`I=I_(0)[exp((eV)/(k_T)-1)]=5xx10^(-12)[e^(23.26)-1]=5xx10^(-12)[1.259xx10^(10)-1]`
`=5xx10^(-12)xx1.259xx10^(10)=0.063A`
If `V=0.7V, then (eV)/(k_T)=(1.6xx10^(-19)xx0.7)/(8.6xx10^(-5)xx1.6xx10^(-19)xx300)=27.14`
`I=I_(0)[exp((eV)/(k_T)-1)]=5xx10^(-12)[e^(27.14)-1]=5xx10^(-12)[6.07xx10^(11)-1]`
`=5xx10^(-12)xx6.07xx10^(11)=3.035A`
:. Increase in current, `DeltaI=(3.035-0.063)=2.972A`
Since, `DeltaI=2.972A, DeltaV=0.7-0.6=0.1V` Dynamic resistance`=(DeltaV)/(DeltaI)=(0.1V)/(2.972A)=0.0336Omega`
As the voltage changes from 1 to 2 V, the current I will be almost equal to `I_(0)(=5xx10^(-12)A)`, showing that the diode possesses practially infinite dynamic resistance in the reverse bias.