Question

In which 120-V light bulb does the filament have greater resistance: a 60-W bulb or a 120-W bulb? If the two bulbs are connected to a 120-V line in series, through which bulb will there be the greater voltage drop? What if they are connected in parallel? Explain your reasoning.

Short answer

When a 60 W bulb is connected in series, it has a higher resistance and voltage drop. Both bulbs have the same voltage drop of 120 V when connected in parallel.

Step-by-step solution

Power

When the voltage across the elements in the circuit is constant, V²/R is used to calculate the power, according to the theory of circuits and power dissipation.

$P=\frac{V^2}{R}$

Voltage drop

Because the resistance R is inversely proportional to the power consumed by the bulb, the higher resistance is for a lower power 60 W bulb. In series, both bulbs have the same current I.

According to ohms law (V = IR), the voltage drop increases as resistance increases, and since 60 W has a higher resistance, the voltage drop is across 60 W.

Both bulbs have the same voltage drop in parallel, and the voltage is 120 V.

Hence, when a 60 W bulb is connected in series, it has a higher resistance and voltage drop. Both bulbs have the same voltage drop of 120 V when connected in parallel.