Question

The brightness of a light bulb depends on the power it dissipates. One expression for calculating power is P=IV. Using these values, account for the fact that the round bulb is so much dimmer than the long bulb.

Answer 1

Okay,

we know that round bulb usually has thicker filament and long bulb usually has thinner filament.

Thicker filament means more cross sectional area and thinner means less cross sectional area

now,

in series, we know current is same in all the elements.

we also know

P = I²R ( joule heating)

and

R = pL / A

where R is resistance and A is cross sectional area

so,

combining above two equations

P_round = (A_long / A _round ) P_long

Therefore,

Power dissipated through Joule heating in the round bulb is less that the power dissipated through Joule heating in the long bulb which means round bulb will be dimmer than the long bulb.