The ratio (R) of output resistance $$r_0$$, and the input resistance $$r_i$$ in measurements of input and output characteristics of a transistor is typically in the range:

We begin by recalling the definitions of the two small-signal resistances that are measured on the common-emitter characteristics of a transistor.

By definition, the input resistance is

$$r_i=\left(\dfrac{\partial V_{BE}}{\partial I_B}\right)_{V_{CE}\;{\text{constant}}},$$

where $$V_{BE}$$ is the base-emitter voltage and $$I_B$$ is the base current. This differential resistance is evaluated on the family of input (base) characteristics. For a silicon transistor biased in its normal active region, the slope $$\partial I_B/\partial V_{BE}$$ is quite steep, so the reciprocal slope, which is the resistance $$r_i$$, is comparatively small. Empirically one encounters

$$r_i \approx 10\ \Omega \text{ to } 100\ \Omega,$$

though values up to a few hundred ohms are also seen, depending on bias current.

Next, the output resistance is

$$r_0=\left(\dfrac{\partial V_{CE}}{\partial I_C}\right)_{I_B\;{\text{constant}}},$$

with $$V_{CE}$$ the collector-emitter voltage and $$I_C$$ the collector current. In the active region, the collector current varies only slightly with $$V_{CE}$$, so the slope $$\partial I_C/\partial V_{CE}$$ is very small and its reciprocal $$r_0$$ is therefore quite large. Typical experimentally measured values are

$$r_0 \approx 10\ \text{k}\Omega \text{ to } 100\ \text{k}\Omega.$$

We are interested in the ratio

$$R=\dfrac{r_0}{r_i}.$$

Substituting the representative numerical ranges just quoted, we write

$$R=\dfrac{10^{4}\ \Omega \ \text{to}\ 10^{5}\ \Omega}{10\ \Omega \ \text{to}\ 10^{2}\ \Omega}.$$

Carrying out the division at the two extremes, we obtain

$$R_{\text{min}}=\dfrac{10^{4}}{10^{2}}=10^{2}, \qquad R_{\text{max}}=\dfrac{10^{5}}{10}=10^{4}.$$

Thus, in typical bias conditions the ratio lies in the decade centred around $$10^{3}$$, most commonly between $$10^{2}$$ and $$10^{3}$$. Expressed as an approximate range we can therefore write

$$R\sim 10^{2}-10^{3}.$$

Comparing this theoretical-empirical result with the choices given, we see that it matches the first option.

Hence, the correct answer is Option A.