Question

A battery that produces a potential difference V is connected to a 10-W light bulb. Later, the 10-W bulb is replaced with a 20-W light bulb. In which case does the battery supply the greatest current? Remember to identify all of your data, write the equation, and show your work.

Answer 1

Answer:

The battery supply the greatest current with the 20-W bulb

Explanation:

The electrical power at a certain time by a two-terminal device is the product of the potential difference between the terminals and the current intensity that passes through the device. For this reason the power is proportional to the current and voltage. Mathematically can be written as:

$P=VI$

Let:

$P_1=Electric\hspace{3}power\hspace{3}dissipated\hspace{3}by\hspace{3}the\hspace{3}10-W\hspace{3}bulb\\P_2=Electric\hspace{3}power\hspace{3}dissipated\hspace{3}by\hspace{3}the\hspace{3}20-W\hspace{3}bulb$

The voltage remains constant for every case so:

$I_1=Current\hspace{3}supply\hspace{3}by\hspace{3}the\hspace{3}battery\hspace{3}with\hspace{3}the\hspace{3}\hspace{3}10-W\hspace{3}bulb\\I_2=Current\hspace{3}supply\hspace{3}by\hspace{3}the\hspace{3}battery\hspace{3}with\hspace{3}the\hspace{3}\hspace{3}20-W\hspace{3}bulb$

Then:

$P_1=V*I_1=10W\\P_2=V*I_2=20W$

Analyzing the equations it makes sense that the battery supplies the highest current with the 20 W bulb, because the power only depends on the voltage and the current, if the voltage remains constant, the only reason for the power to increase is due to current.