Given that wall voltage is 120 Volts RMS, and each light is 8 ohms, and that there are 4 strands of 50 Lights as shown in the figure then A) What is the RMS voltage across each individual light? A) How much current will be coming through the plug from the electrical outlet? B) How much power will be used by the light set?
we can consider each strand of 50 identical resistors as a single equivalent resistance, and then calculate the overall equivalent resistance of the four strands in parallel. Then, we can use Ohm's Law to calculate the current and voltage across each individual resistor.
To find the equivalent resistance of one strand of 50 resistors, we can use the formula for the resistance of resistors in series:
R_eq = R1 + R2 + ... + Rn
where R1, R2, ..., Rn are the resistances of each individual resistor. Since each resistor has a resistance of 8 ohms, the equivalent resistance of one strand is:
R_eq = 8 + 8 + ... + 8 (50 times) = 400
To find the equivalent resistance of the four strands in parallel, we can use the formula for the resistance of resistors in parallel:
1/R_eq = 1/R1 + 1/R2 + ... + 1/Rn
where R1, R2, ..., Rn are the resistances of each individual strand. Since there are four strands, the equivalent resistance is:
1/R_eq = 1/400 + 1/400 + 1/400 + 1/400 = 4/400
R_eq = 100
Now, using Ohm's Law, we can calculate the current and voltage across each individual resistor. The total current through the circuit is:
I = V/R_eq = 120/100 = 1.2 A
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
