Chapter 35, Problem 17A

The circuit below contains resistors $R_1$, $R_2$, and $R_3$.

Rank the following combinations of resistances in terms of the current measured by the ammeter, from highest to lowest.

(A) $R_1=1\Omega ,R_2=2\Omega ,R_3=3\Omega$

(B) $R_1=2\Omega ,R_2=1\Omega ,R_3=2\Omega$

(C) $R_1=3\Omega ,R_2=3\Omega ,R_3=1\Omega$

To determine

Ranking of the different combinations of the resistances in terms of current from the ammeter in the circuit.

Answer to Problem 17A

The ranking of combination of resistances A, B, and C from highest to lowest is C, A, B.

Explanation of Solution

Given info:

(A) $R_1=1\Omega$ , $R_2=2\Omega$ , $R_3=3\Omega$

(B) $R_1=2\Omega$ , $R_2=1\Omega$ , $R_3=2\Omega$

(C) $R_1=3\Omega$ , $R_2=3\Omega$ , $R_3=1\Omega$

Formula Used:

The expression to calculate the total resistance of circuit for combination (A) is,

  $R_A=R_1+R_2+R_3$

The expression to calculate the total resistance of circuit for combination (B) is,

  $R_B=R_1+R_2+R_3$

The expression to calculate the total resistance of circuit for combination (C) is,

  $R_C=R_1+R_2+R_3$

Calculation:

Substitute the values in the above expression.

  $\begin{array}{c}{R}_A=1\Omega +2\Omega +3\Omega \\ =6\Omega \end{array}$

Substitute the values in the above expression.

  $\begin{array}{c}{R}_B=2\Omega +1\Omega +2\Omega \\ =5\Omega \end{array}$

Substitute the values in the above expression.

  $\begin{array}{c}{R}_A=3\Omega +3\Omega +1\Omega \\ =7\Omega \end{array}$

The total circuit resistance for the combination (C) is highest, total circuit resistance for the combination (B) is least and total circuit resistance for the combination (A) is between highest and lowest circuit current.

Conclusion:

Thus, the ranking of combination of resistances A, B,C from highest to lowest is C, A, B.