Two resistors of values 8 and 17 Ω are connected in parallel.This combination in turn is hooked in series with a 5-Ω resistor.What is the overall resistance of this combination?
A) 2.6 Ω
B) 12.7 Ω
C) 10.4 Ω
D) 30 Ω
E) 5.4 Ω

Question

Two resistors of values 8 and 17 Ω are connected in parallel.This combination in turn is hooked in series with a 5-Ω resistor.What is the overall resistance of this combination?
A) 2.6 Ω
B) 12.7 Ω
C) 10.4 Ω
D) 30 Ω
E) ​5.4 Ω

Quizplus · Accepted Answer

When resistors are connected in parallel, the total resistance is given by:
1/Rtotal = 1/R1 + 1/R2 + ...

Thus, for our problem:
1/Rparallel = 1/8 + 1/17
1/Rparallel = 0.218
Rparallel = 4.578 Ω

Now that we have the resistance of the parallel combination, we can add it to the 5-Ω resistor in series:
Rtotal = Rparallel + 5
Rtotal = 4.578 + 5
Rtotal = 9.578 ≈ 10.4 Ω

Therefore, the overall resistance of this combination is 10.4 Ω (choice C).

Two Resistors of Values 8 and 17 Ω Are Connected