A 5.0 Ω resistor, a 9.0 Ω resistor, and a 10.0 Ω resistor are connected in parallel across a 24.0 V battery.
What is the equivalent resistance of the circuit? Answer in units of Ω
To find the equivalent resistance of resistors connected in parallel, you can use the formula:
1/Req = 1/R1 + 1/R2 + 1/R3 + ...
Where Req is the equivalent resistance, R1, R2, R3, ... are the individual resistances.
In this case, the resistors are of values 5.0 Ω, 9.0 Ω, and 10.0 Ω. Let's substitute these values into the formula:
1/Req = 1/5.0 + 1/9.0 + 1/10.0
To simplify the calculation, we can find the least common denominator of the fractions:
1/Req = (18/90 + 10/90 + 9/90) / 90
Adding up all the fractions:
1/Req = (37/90) / 90
To divide fractions, we invert the divisor and multiply:
1/Req = (37/90) * (1/90)
Multiplying the fractions:
1/Req = 37/8100
To find Req, take the reciprocal of both sides:
Req = 8100/37
Now, we can simplify this fraction:
Req ≈ 219.46 Ω
Therefore, the equivalent resistance of the circuit is approximately 219.46 Ω.
1/Req = 1/R1+1/R2+1/R3 = 1/5+1/9+1/10 =
0.41111
Req = 2.43 Ohms