Algebraic Substitution for Electric Circuits

Though this “current divider formula” may be found in any number of electronics reference books, your students need to understand how to algebraically manipulate the given formulae to arrive at this one.

At first it may seem as though the two divider formulae (voltage versus current) are easy to confuse. Is it \(\frac {R}{R_{total}}\) or \(\frac {R_{total}}{R}\) ? However, there is a very simple way to remember which fraction belongs with which formula, based on the numerical value of that fraction. Mention this to your students and at least one of them will be sure to recognize the pattern.

This question is nothing more than an exercise in algebraic manipulation.

Solving this algebraic problem requires both manipulation of the temperature equation and substitution of variables. One important detail I incorporated into this question is the lack of a subscript for T in the original resistance formula. In the first sentence I identify that temperature as being in degrees Celsius, but since there is no other T variables in the equation, I did not have to include a “C” subscript. When students look to the Celsius-Fahrenheit conversion formula to substitute into the resistance formula, they must decide which T in the conversion formula to use, T_F or T_C. Here, I purposely wrote the conversion formula in terms of T_F to see how many students would blindly substitute T_F for T in the resistance formula instead of properly identifying T_C as the variable to substitute and doing the work of manipulation.

Far from being a “trick” question, this scenario is very realistic. Formulae found in reference manuals do not necessarily use standardized variables, but rather cast their variables according to context. Multiple formulae will most likely not be written with identical subscripted variables just waiting to be substituted. It is the domain of the intelligent technician, engineer, or scientist to figure out what variables are appropriate to substitute based on context!