Calculating the Current in a Single-Loop Circuit — Question 3

Question 3

Two load tests determine a source model without a voltmeter

A source drives 2.00 A through a 5.00 ohm load and 1.00 A through an 11.0 ohm load. Its emf E and internal resistance r are unchanged between tests.

1. Infer E and r from the loop equations.

2. Predict the current for a 2.00 ohm load and determine whether the inferred r is physically admissible.

Question 3 - Solution

Two load tests determine a source model without a voltmeter

(a) Method and calculation

$$E=2(5+r),\quad E=1(11+r).$$$$10+2r=11+r\Rightarrow r=1.00\,\Omega,\quad E=12.0\,\mathrm V.$$

(b) Interpretation and further calculation

$$I(2.00\,\Omega)=12.0/(2.00+1.00)=4.00\,\mathrm A.$$$$r=1.00\,\Omega>0\quad\text{is compatible with a passive internal resistance}.$$

Physical check

Different loads supply independent constraints; one current measurement would leave E and r underdetermined.