Animated Solution for Physics - Semiconductors: In the given circuit, the current through zener diode is close to

When dealing with Zener diode circuits, the most robust strategy is to use proof by contradiction. We start by assuming the Zener diode is in its breakdown region. If this assumption leads to a physically impossible scenario, we know the diode is actually off.

Let's assume the Zener diode is in breakdown. This clamps the voltage across the entire parallel section to exactly $V_z=10\text{ V}$.

Since the total source voltage is $12\text{ V}$, the remaining voltage must drop across the series resistor $R_1$.

Now, we can find the total current supplied by the battery, which flows entirely through $R_1$:

Next, let's look at the two $R_2$ resistors. They are both $1500\Omega$ and are connected in parallel. Their equivalent resistance is:

If the voltage across this parallel combination is indeed $10\text{ V}$, the current required by these resistors alone would be:

Here is where the physics breaks down. The main branch is only supplying $4\text{ mA}$ of current. However, the parallel resistors are demanding $13.33\text{ mA}$ to maintain the $10\text{ V}$ drop.

By Kirchhoff's Current Law, the current through the Zener diode would have to be:

A negative current implies the Zener diode is acting as a power source, which is impossible for a passive component in this configuration.

Because our assumption led to a contradiction, the Zener diode never reached the breakdown voltage. It remains reverse-biased but non-conducting, acting effectively as an open circuit.

Therefore, the current through the Zener diode is exactly zero.