A non-ideal battery with internal resistance r is connected as shown to a collec

Question

A non-ideal battery with internal resistance r is connected as shown to a collection of eight identical light bulbs, each with the same resistance R. Known values: = 120 V r = 0.01 Ohm R = 3.00 Ohm Rank the brightnesses of the bulbs, from brightest to dimmest. Suppose that bulb 1 could be exchanged for a new variety of bulb that is identical to the original in every respect except that its filament is 25% longer and 25% thicker (greater diameter). By what percentage would Delta V_i (the voltage difference across bulb 1) change? Referring to the original circuit (as shown above): You are now offered a choice of removing either the straight wire A or the straight wire B. Which action would result in a larger change in the total current supplied by the battery (and what kind of change-an increase or a decrease)? Be sure to show all work and calculations for each alternative.

Explanation / Answer

a)

1>2=3>4=5=6=7

b)

initially voltage across 1st bulb

V1 = E/r+R+0.5R

V1 = 26.61 Volts

when filament is increased by 25 percent and diameter is increased by 25 percent

New resistance

R1 = 1.25R/1.25^2 = 3/1.25 = 2.5 ohm

now voltage across 1 is

V1' = E/2.5+3+0.01

V1' = 29.925 Volts

percentage voltage = (V1' -V1/V1 )x100 = 12.45 percentage

c)

removing B will change resistance very large so answer is B

current decreases

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