Concept of "resistance" and "power dissipation" in a transistor - Explanation?
The power in any electrical circuit is the product of current and voltage:

$$ P = IE $$

This holds for any individual component (resistors, MOSFETs, BJTs) or entire circuits (cell phones, radios, computers). In the case of resistors, or things that look close enough to resistors (like MOSFET channels), then voltage and current are related by a constant (the resistance), so we can calculate one from the other, so we only need to know any two of the voltage, current, and resistance:

$$ P = IE = I^2 R = E^2/R $$

For everything else we either need to know both the current and the voltage, or have some other function that allows us to calculate one from the other. However, power is still just the product of current and voltage.

For BJTs, we can usually neglect the power from the base current because it's much smaller than the collector current. If so, then all we really care about is the collector-emitter voltage \$ V_{ce} \$ and the collector current \$I_c\$.

The datasheet will give the details about how \$ V_{ce} \$ relates to \$I_c\$. Here's BC547:



You can see that if you hold the base current constant, then \$ V_{ce} \$ is not a linear function of \$ I_c \$, as it would be if the collector-emitter was a resistance. You can also see that if you hold \$I_c\$ constant, then increasing the base current can make \$V_{ce}\$ lower, up to a point.

For example, let's say our base current is \$50 \mu A\$, so we use the lowest line. Say collector current is \$10mA\$. It looks like those lines intersect at about \$0.25V\$, so the power is:

$$ 0.25 V * 10mA = 2.5mW $$