Chapter 35, Problem 16A

The resistors in the circuits below are all identical. Rank the circuits according to the size of the equivalent resistance for each, from most resistance to least resistance.

To determine

The ranking of the given electric circuits according to the equivalent resistance of the circuit from most to least.

Explanation of Solution

Introduction:

In a series circuit, the resistances are added simply. So, the equivalent resistance of the circuit become more than the individual resistances. In a parallel circuit, the resistances are added by adding the inverse of individual resistances. So, the equivalent resistance of the circuit becomes less than the individual resistances of the parallel connection.

In circuit A, two equivalent resistances are connected in series. So, the total equivalent resistance of the circuit A is two times of the equivalent resistance.

In circuit B, three equivalent resistances are connected in series. So, the total equivalent resistance of the circuit B is three times of the equivalent resistance.

In circuit C, the total equivalent resistance is one third of the equivalent resistance.

Conclusion:

The rank of the equivalent resistances from most to least is Circuit B, Circuit A and Circuit C.