Question

Three resistors in parallel have an equivalent resistance of 15 Ω. Two of the resistors have resistances of 30 Ω and 40 Ω. What is the resistance of the third resistor?

1) 10 Ω
2) 15 Ω
3) 20 Ω
4) 25 Ω

Answer 1

To find the third resistor's resistance in a parallel circuit with an equivalent resistance of 15 Ω and two known resistors of 30 Ω and 40 Ω, we apply the formula for parallel resistors and solve to find that the third resistor has a resistance of 120 Ω.

Step-by-step explanation:

To find the resistance of the third resistor when three resistors are connected in parallel with an equivalent resistance of 15 Ω, we use the formula for parallel resistors:

1/Rtotal = 1/R1 + 1/R2 + 1/R3

Where Rtotal is the equivalent resistance, R1 and R2 are the known resistances, and R3 is the unknown. Given R1 = 30 Ω, R2 = 40 Ω, and Rtotal = 15 Ω, we calculate:

1/15 = 1/30 + 1/40 + 1/R3

After solving for 1/R3, we find R3 by taking the reciprocal. The calculation gives R3 = 120 Ω, making the correct answer (1) 120 Ω.