Five resistors each have resistance R.Three of the resistors are connected in series and this combination is then connected in parallel with the two other resistors which have been connected in series with each other.What is the equivalent resistance for this arrangement?

Question

Quizplus · Accepted Answer

When three resistors are connected in series, their equivalent resistance is simply the sum of their individual resistances. Therefore, the three resistors in series have an equivalent resistance of 3R.

When two resistors are connected in series, their equivalent resistance is the sum of their individual resistances. Therefore, the two resistors in series have an equivalent resistance of 2R.

The final step is to find the equivalent resistance of the entire circuit, which involves combining the two groups of resistors that are connected in parallel. When resistors are connected in parallel, their equivalent resistance can be found using the formula:

1/Req = 1/R1 + 1/R2 + 1/R3 + ...

In this case, we have two parallel groups of resistors, each with an equivalent resistance:

Req1 = (3R) 
Req2 = (2R)

So the total equivalent resistance, Req, is:

1/Req = 1/Req1 + 1/Req2 
1/Req = 1/(3R) + 1/(2R) 
1/Req = (2+3)/(6R) 
1/Req = 5/(6R) 
Req = (6R/5)

Therefore, the equivalent resistance for this arrangement is:

Req = (6R/5)

Which matches answer choice B.

Five Resistors Each Have Resistance R