R1= 10 ohm
R2= 20 ohm
R3= 50 ohm
R4= ???
R1, R2, R3 and R4 are connected in parallel across a 120 V "power" supply to generate a current of 21 Amps. The value of R4 is most nearly _____ ohms.
0, 5, 10, 16, 100, 200, 300
I think 5 ohms, but I'm not sure...In need of some assistance, please
R(combined) = 120/21 = 5.71 ohms
1/5.714 = 1/10 + 1/20 + 1/50 + 1/R4
= 0.175 + 1/R4
0.175 = 1/R4 + 0.170
1/R4 = 0.005
R4 = ___
It's not 5 ohms
To find the value of R4, we can use Ohm's Law and the principle of parallel resistors.
Given:
R1 = 10 ohms
R2 = 20 ohms
R3 = 50 ohms
Voltage (V) = 120 V
Current (I) = 21 Amps
To calculate the total resistance of the parallel combination of R1, R2, R3, and R4, we can start by finding the equivalent resistance of R1, R2, and R3.
The formula for the total resistance of resistors connected in parallel is given by:
1/R_total = 1/R1 + 1/R2 + 1/R3 + 1/R4
Substituting the given values:
1/R_total = 1/10 + 1/20 + 1/50 + 1/R4
To solve for R_total, we need to find the least common denominator and simplify the equation. The least common denominator for 10, 20, and 50 is 100; therefore, the equation becomes:
1/R_total = 10/100 + 5/100 + 2/100 + 1/R4
1/R_total = (10 + 5 + 2)/100 + 1/R4
1/R_total = 17/100 + 1/R4
Now, let's calculate the value of R_total:
R_total = 1 / (17/100 + 1/R4)
R_total = 1 / (17/100) + 1/R4
R_total = 100 / 17 + 1/R4
R_total = (100R4 + 17) / (17R4)
We know that voltage (V) = current (I) * resistance (R). Using Ohm's Law, we can write:
V = I * R_total
Substituting the given values, we get:
120 = 21 * R_total
Now, solve for R_total:
R_total = 120 / 21
R_total ≈ 5.71 ohms
Since the given answer options are discrete values, we have to find the closest value to 5.71 ohms. The closest value to 5.71 ohms from the given answer options is 5 ohms. Therefore, the value of R4 is most nearly 5 ohms.
So, your initial guess of 5 ohms is correct!