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DC Bridge Circuits
19 questions By Tony R. Kuphaldt
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Question 4 of 19
How much voltage needs to be dropped across resistor R1 in order to make voltage VAB equal to zero?
How much resistance must R1 possess in order to drop that amount of voltage?
Reveal answerVR1 = 9 V
R1 = 20 kΩ
Follow-up question: what do you notice about the four resistors’ values in this condition where VAB = 0? Pair up these four resistors into two sets of two pairs, and calculate the ratios of those pairs. What do you notice about these ratios?
Notes:The follow-up question regarding ratios is a good introduction to the fundamental principle of balanced bridge circuits. Having students work through the calculations together is a good way for them to see the principle for themselves.
It is also important to note in this circuit which ratios are not in agreement with each other. You can’t just divide these four resistors into any set of two pairs and expect the ratios to equal each other! It is very important for students to see this, as well.
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Question 5 of 19
A thermistor is a special resistor that dramatically changes resistance with changes in temperature. Consider the circuit shown below, with two identical thermistors:
The “ to” label in each one shows that they both have positive α coefficients.
How much voltage would you expect the voltmeter to register when the two thermistors are at the exact same temperature? Which thermistor would have to become hotter in order to cause the voltmeter to read a significant negative voltage?
Reveal answerIf the two thermistors are at equal temperature, the voltmeter should register 0 volts. To get the voltmeter to register negative, the left-hand thermistor would have to be warmer than the right-hand thermistor.
Notes:This circuit may be viewed from the perspective of it being two voltage dividers, or from the perspective of being a current divider. Either way, it is a good exercise for you and your students to explore how it functions.
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Question 6 of 19
In general terms, describe what must be done to balance this bridge circuit. What, exactly, does the term “balance” mean in this context?
Also, write an equation containing only the four resistor values (R1, R2, R3, and R4) showing their relationship to one another in a balanced condition.
Reveal answerFor a bridge circuit to be “balanced” means that there is zero voltage between the two opposite corners of the circuit (where the battery does not) connect. Achieving a condition of “balance” in a bridge circuit requires that the resistance ratios of the four “arms” of the circuit be in proportion:
R1 R3= R2 R4Follow-up question: the bridge-balance equation shown above may also be written in a slightly different form:
R1 R2= R3 R4Show algebraically how the first equation may be manipulated to take the form of the second equation, thus demonstrating these two equations’ equivalence.
Notes:Challenge your students to write a “balance equation” describing how the ratios must relate to each other in order to achieve balance.
