Question

A lightbulb is rated by the power that it dissipates when connected to a given voltage. For a lightbulb connected to 120 V household electricity, decreasing the resistance of the filament will _____ the current through the bulb and _____ the power dissipated by the bulb.

Decrease, decrease
Decrease, increase
Increase, increase
Increase, decrease

Answer 1

Answer:

Increase, increase

Explanation:

For a light bulb, voltage, resistance and current follows the Ohm's law:

$V=RI$

where

V is the voltage

R is the resistance

I is the current

In this problem, the voltage is fixed: V=120 V. We can rewrite the equation as

$I=\frac{V}{R}$ (1)

we see that the current is inversely proportional to the resistance: so, if we decrease the resistance of the filament, the current will increase.

Moreover, the power dissipated by the bulb is

$P=I^2 R$

which can be rewritten using (1) as

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

We see that the power dissipated is inversely proportional to the resistance: therefore, if we decrease the resistance of the filament, the power dissipated will increase.