Complete Question
What is the minimum number of 20-amp 277-volt branch circuits required where 810 incandescent luminaries are to be installed?The lamps to be installed are rated 75 watts at 277 volts. This is NOT a continuous load so each circuit can carry 20 amps maximum
Answer:
The number is [tex]k = 11[/tex]
Explanation:
From the question we are told that
The current is [tex]I = 20 \ A[/tex]
The voltage is [tex]V = 277 \ volt[/tex]
The power rating of each bulb is [tex]P = 75 \ W[/tex]
The total number of incandescent luminaries is [tex]n = 810[/tex]
Generally the amount of current each lamp takes is mathematically represented as
[tex]I_e = \frac{P}{ V}[/tex]
=> [tex]I_e = \frac{75}{ 277}[/tex]
=> [tex]I_e = 0.270 \ A[/tex]
Generally the number of bulb fitting(i.e bulbs ) a 20 A current can supply (i.e the bulbs the branch ) to is
[tex]N = \frac{I}{I_e}[/tex]
=> [tex]N = \frac{20 }{ 0.270 }[/tex]
=> [tex]N = 73.86[/tex]
Generally the number of 20-amp 277-volt branch circuits required is mathematically represented as
[tex]k = \frac{n}{N}[/tex]
=> [tex]k = \frac{810}{73.86}[/tex]
=> [tex]k = 11[/tex]
