Two resistors of values 6.0 and 14.0 Ω are connected in parallel.This combination in turn is hooked in series with a 2.0-Ω resistor.What is the overall resistance of this combination?
A)1.4 Ω
B)11 Ω
C)6.2 Ω
D)22 Ω
E)4.2 Ω

Question

Quizplus · Accepted Answer

The formula for calculating the total resistance of resistors connected in parallel is:

1/Rt = 1/R1 + 1/R2 + ...

where R1, R2, etc. are the values of each individual resistor.

Using this formula, we can find the equivalent resistance of the 6Ω and 14Ω resistors in parallel:

1/Rp = 1/6Ω + 1/14Ω
1/Rp = 0.1667 + 0.0714
1/Rp = 0.2381
Rp = 4.2 Ω

Now that we have the equivalent resistance of the parallel combination, we can use the formula for resistors in series to find the total resistance:

Rt = Rp + R3
Rt = 4.2Ω + 2.0Ω
Rt = 6.2 Ω

Therefore, the overall resistance of this combination is 6.2 Ω, which corresponds to choice C.

Two Resistors of Values 6