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Algebraic Equation Manipulation for Electric Circuits
19 questions By Tony R. Kuphaldt
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Question 1 of 19
The electrical resistance of a conductor at any temperature may be calculated by the following equation:
$$R_T = R_r + R_raT - R_raT_r$$
Where,
RT = Resistance of conductor at temperature T
Rr = Resistance of conductor at reference temperature Tr
α = Temperature coefficient of resistance at reference temperature Tr
Simplify this equation by means of factoring.
Reveal answer$$R_T = R_r [1+a(T-T_r)]$$
Follow-up question: when plotted on a graph with temperature (T) as the independent variable and resistance (RT) as the dependent variable (i.e. a two-axis graph with T on the horizontal and R on the vertical), is the resulting plot linear? Why or why not? How is it possible to tell just by looking at the equation, prior to actually plotting on a graph?
Notes:Just an exercise in algebra here!
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Question 2 of 19
The equation for voltage gain (AV) in a typical non-inverting, single-ended opamp circuit is as follows:
$$A_V = \frac{R_1}{R_2} + 1$$
Where,
R1 is the feedback resistor (connecting the output to the inverting input)
R2 is the other resistor (connecting the inverting input to ground)
Suppose we wished to change the voltage gain in the following circuit from 5 to 6.8, but only had the freedom to alter the resistance of R2:
Algebraically manipulate the gain equation to solve for R2, then determine the necessary value of R2 in this circuit to give it a voltage gain of 6.8.
Reveal answer$$R_2 = \frac{R_1}{A_V-1}$$
For the circuit shown, R2 would have to be set equal to 810.3 Ω.
Notes:Nothing more than a little algebra to obtain the answers for this question!
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Question 3 of 19
The equation for voltage gain (AV) in a typical inverting, single-ended opamp circuit is as follows:
AV = R1 R2Where,
R1 is the feedback resistor (connecting the output to the inverting input)
R2 is the other resistor (connecting the inverting input to voltage signal input terminal)
Suppose we wished to change the voltage gain in the following circuit from 3.5 to 4.9, but only had the freedom to alter the resistance of R2:
Algebraically manipulate the gain equation to solve for R2, then determine the necessary value of R2 in this circuit to give it a voltage gain of 4.9.
Reveal answerR2 = R1 AVFor the circuit shown, R2 would have to be set equal to 1.571 kΩ.
Notes:Nothing more than a little algebra to obtain the answers for this question!
Question 14, Equation 2 - the ‘+’ symbol is missing between ‘a 3’.
Question 17, right-hand equation - the square-root should only be over the left side of the equation.
Question 19, Hint - the ‘+’ symbol is missing between ‘I 0.005’.
They do seem to be correct in the equivalent questions in the PDF version though.
In the answer to question 8, the second solution has R1 on the right side of the equation when it should be R.