Answer :
A string of fifty 15 ohm Christmas tree light are connected in parallel. One burns out, the rest will stay lit. The total resistance is 4.5 ohms.
When resistors are connected in parallel, the total resistance is calculated using the formula:
[tex]1/R_T_o_t_a_l=1/R_1+1/R_2+1/R_3+....+1/R_n[/tex]
In this case, we have fifty Christmas tree lights connected in parallel, each with a resistance of 15 ohms.
[tex]1/R_T_o_t_a_l=1/15+1/15+1/15+....+1/15(fifty times)\\1/R_T_o_t_a_l=(50/15)*(1/15)\\\\1/R_T_o_t_a_l=4.5 ohms\\[/tex]
Therefore, the total resistance of the fifty Christmas tree lights connected in parallel is 4.5 ohms.
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Final answer:
The total resistance of the fifty 15 ohm Christmas tree lights connected in parallel is 0.3 ohms.
Explanation:
In a parallel circuit, the total resistance is given by the formula: 1/Req = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn. In this case, we have fifty 15 ohm resistors connected in parallel, so the formula becomes: 1/Req = 1/15 + 1/15 + ... + 1/15 (total of fifty terms).
Since all of the resistors are the same (15 ohms), we can simplify the equation to: 1/Req = 50/15
Simplifying further, we find that the total resistance is: Req = 15/50 = 0.3 ohms.
