Total resistance decreases:
1/R(total) = 1/R1 + 1/R2 + 1/R3
Assuming each lightbulb has the same resistance: R1 = R2 = R3
1/R(total) = 1/R = 1/R + 1/R = 3/R
R(total) = R/3
Before the bulb was added:
1/R(total) = 1/R + 1/R = 2/R
R(total) = R/2
R/3 < R/2
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