Q.Obtain an expression for anode current $I_A$ when $I_G = 0$.

Using the two-transistor model of the SCR (a pnp and an npn transistor interconnected) and adding their collector currents, the anode current with zero gate current can be derived. …

[!TLDR]

Add the two collector currents of the equivalent pnp and npn transistors to get $I_A=\dfrac{I_{co1}+I_{co2}}{1-(\alpha_1+\alpha_2)}$ when $I_G=0$.

The SCR can be represented by its two-transistor equivalent: a pnp transistor $T_1$ and an npn transistor $T_2$ interconnected so that the collector of each drives the base of the other. Let $\alpha_1$ and $\alpha_2$ be their common-base current gains and $I_{co1}$ and $I_{co2}$ their leakage (collector-base saturation) currents.

The collector current of each transistor is:

With no gate current, $I_G=0$, the anode and cathode currents are equal, $I_A=I_K$.

The anode current is the sum of the two collector currents:

Collecting the $I_A$ terms:

Therefore …