Suppose you have three identical lightbulbs, some wire, and a battery. You connect one lightbulb to the battery and take note of its brightness. You add a second lightbulb, connecting it in parallel with the previous light bulbs, again take note of the brightness. Repeat the process with the third lightbulb, connecting it in parallel with the other two. As the lightbulbs are added, how are the following properties affected?

a. Brightness of the bulb
i. Increases
ii. decreases
iii. remains
iv. unchanged

b. Individual currents in the bulb
i. Increases
ii. decreases
iii. remains
iv. unchanged

c. Power delivered by the battery
i. Increases
ii. decreases
iii. remains
iv. unchanged

d. Lifetime of the battery
i. Increases
ii. decreases
iii. remains
iv. unchanged

a) The brightness of the light bulb **remains unchanged** as the number of bulbs increases.

b) The individual currents of the lighbulbs, **decreases** as the number of bulbs increases.

c) Power delivered by the battery **increases** as the number of light bulbs increases.

d) Lifetime of the battery **decreases** as the number of light bulbs increases.

Explanation:

When resistors (in form of the light bulbs) are connected in parallel, there exists the same voltage across each of the resistors and this voltage is equal in magnitude to the voltage of the source (battery in this case).

But the current in each resistor varies, depending on their indivudyal resistance. The sum of the current in the resistors is equal to the sum of current produced by the source. This means that the current in each resistor (lightbulb) decreases as the number of resistors increases.

a) The brightness of the bulb.

The brightness of the bulb is an indication of the potential difference across the bulb. And since this stays constant for each branch of a parallel connection, the brightness remains constant.

b) Individual Currents of the lightbulbs

I have explained earlier that in a parallel connection, the individual branches share the current with respect to the resistance of each branch. So, as the number of light bulbs increases, the individual currents of the lighbulbs, decreases.

c) Power delivered by the battery is given as IV. where I is total current delivered and V is the voltage of the source. As the number of light bulbs increases, a parallel connection ensures that the overall resistance of the setup decreases. And since the voltage of the power source is constant, decreasing resistance leads to increasing total current produced by power source, thereby leading to an increase in the power delivered by the source.

d) Lifetime of the battery depends on the rate of power dissipation. If the increase in light bulbs would lead to an increase in power dissipated, then the lifetime of the battery reduces.

do you have a formula possibly

there are no atoms