Calculating the Current in a Single-Loop Circuit — Question 5

Question 5

A rheostat must cover both required current endpoints

A source E=15.0 V has internal resistance r=1.00 ohm. It drives a fixed 4.00 ohm resistor in series with an adjustable rheostat X. The required current range is .500 A to 2.00 A.

1. Find the required minimum and maximum X.

2. Find the largest current possible with a nonnegative X and explain why no rheostat setting can exceed it.

Question 5 - Solution

A rheostat must cover both required current endpoints

(a) Method and calculation

$$I=E/(r+R+X)\Rightarrow X=E/I-r-R.$$$$X_{\min}=15/2-5=2.50\,\Omega,\quad X_{\max}=15/.5-5=25.0\,\Omega.$$

(b) Interpretation and further calculation

$$X\ge0\Rightarrow r+R+X\ge5.00\,\Omega.$$$$I\le15/5=3.00\,\mathrm A.$$

Physical check

The rheostat changes resistance; it cannot cancel the positive fixed resistance in a passive loop.