Question: [![enter image description here](https://i.stack.imgur.com/UBFqR.png)](https://i.stack.imgur.com/UBFqR.png)
The supply voltage is 15 V and RL is 100 kΩ. Find the voltage across each diode and RL.

Is = 0.1 μA, η = 2, and VT = 25 mV.

How can I calculate the net current through RL? I have three unknowns: the net current and the voltages across the diodes.

Answer: 
You'd use the Shockley equation,
$$ I(V\_D)=I\_S \left( e^\frac{V\_D}{\eta V\_T} - 1 \right), $$
to figure it out.

You're given \$I\_S\$, \$V\_T\$ and \$\eta\$.

We can invert this equation: given \$I\$, solve for \$V\_D\$. This will be more useful, since the current \$I\$ is the same for both diodes:

$$
V\_D(I) = \ln \left( \frac{I}{I\_S}+1 \right) {\eta V\_T}
$$

Now, the diode D2 is in reverse saturation, since the voltage across it is on par with \$-\frac{1}{\eta V\_T}\$. The reverse saturation current is then \$-I\_S\$, and that diode acts as a current limiter, and sets the current in the entire circuit.

Then, the voltage drop on the resistor is \$I\_S \cdot R\_L\$, the voltage drop on D1 is, per Schockley equation, \$V\_{D1}=\ln(2)\eta V\_T\$, and the voltage drop across D2 is whatever voltage is left in the circuit.

We can simulate it and see if it agrees with our figuring:

![schematic](https://i.stack.imgur.com/6a9uB.png)

[simulate this circuit](/plugins/schematics?image=http%3a%2f%2fi.stack.imgur.com%2f6a9uB.png) – Schematic created using [CircuitLab](https://www.circuitlab.com/)

The diode models in the simulation have had their \$I\_S\$ and \$n\equiv\eta\$ set according to the values given in the assignment. The thermal voltage is slightly different since the value used by CircuitLab is not exactly 25mV, but we see that the simulation and the computed results agree to within 1mV or so.
The voltage across the forward-biased diode is going to be less than 0.7V (the forward voltage with substantial current). If you look at the Shockley diode equation, the current with a large negative voltage (relative to \$\eta\$ Vt) will be essentially -Is. So you can then calculate the forward voltage of the forward biased diode and the voltage across the resistor and verify that the assumptions are correct. Since RL is relatively low resistance, it will be correct. If RL was, say 1G ohm it would not be correct.