Three identical light bulbs are connected in series to the same battery as shown

Question

Three identical light bulbs are connected in series to the same battery as shown in the figure.

(a) If a fourth identical light bulb is added in series, does the total current coming from the battery increase, decrease, or stay the same? Explain briefly.

(b) If a fourth identical light bulb is added in series, does the brightness of the original three bulbs increase, decrease, or stay the same? Explain briefly

I understand the concept but have trouble when trying to prove mathematically. Thanks for the help

Explanation / Answer

(a)

the total current coming from the battery is same because all bulbs have identical resitance

using Ohm's law (V = I • R), the current in the battery and thus through every resistor can be determined by finding the ratio of the battery voltage and the equivalent resistance.

Ibattery = I1 = I2 = I3 =I4= Vbattery / Req

(b)

the formula power across bulb is

P = I^2 R

since I and resitance of each bulb is same so power is also same ( brighness)

the brightness of the original three bulbs stay the same

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