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Simultaneous Equations for Circuit Analysis
25 questions By Tony R. Kuphaldt
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Question 19 of 25
The voltage gain of a common-emitter transistor amplifier is approximately equal to the collector resistance divided by the emitter resistance:
Knowing this, calculate the necessary resistance values for the following fixed-value resistors (R1 and R2) to give this common-emitter amplifier an adjustable voltage gain range of 4 to 7:
Reveal answerR1 = 13.33 kΩ
R2 = 3.333 kΩ
Notes:Have your students show how they set up the system of equations to solve for the two resistor values. This is a good exercise to do in front of the class, so everyone can see (possibly) different methods of solution.
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Question 20 of 25
Suppose you needed to choose two resistance values to make a voltage divider with a limited adjustment range. One of these resistors will be fixed in value (R1), while the other will be variable (a potentiometer connected as a rheostat- R2):
Set up a system of simultaneous equations to solve for both R1 and R2, and show how you arrived at the solutions for each.
Hint: remember the series resistor voltage divider formula . . .
$$V_R = V_{total} (\frac{R}{R_{total}})$$
Reveal answerR1 (fixed) = 4.286 kΩ
R2 (pot) = 19.048 kΩ
Follow-up question: you will not be able to find a potentiometer with a full-range resistance value of exactly 19.048 kΩ. Describe how you could take a standard-value potentiometer and connect it to one or more fixed-value resistors to give it this desired full-scale range.
Notes:Be sure to have your students set up their equations in front of the class so everyone can see how they did it. Some students may opt to apply Ohm’s Law to the solution of both resistors, which is good, but for the purpose of developing equations to fit problems it might not be the best solution. Challenge your students to come up with a set of equations that solve for R1 and R2, then use techniques for solution of simultaneous equations to arrive at solutions for each.
The follow-up question is very practical, as it is impossible to find potentiometers ready-made to arbitrary values of full-scale resistance. Instead, you must work with what you can find, which is usually nominal values such as 10 kΩ, 50 kΩ, 100 kΩ, etc.
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Question 21 of 25
Suppose you needed to choose two resistance values to make a voltage divider with a limited adjustment range:
Set up a system of simultaneous equations to solve for both R1 and R2, and show how you arrived at the solutions for each.
Hint: remember the series resistor voltage divider formula . . .
$$V_R = V_{total} (\frac{R}{R_{total}})$$
Reveal answerR1 = 5.25 kΩ
R2 = 2.25 kΩ
Notes:Be sure to have your students set up their equations in front of the class so everyone can see how they did it. Some students may opt to apply Ohm’s Law to the solution of both resistors, which is good, but for the purpose of developing equations to fit problems it might not be the best solution. Challenge your students to come up with a set of equations that solve for R1 and R2, then use techniques for solution of simultaneous equations to arrive at solutions for each.
