This lab exercise is ©2002 by Ren Colantoni. You are welcome to use it for any non-profit educational purpose to which it may apply. Just don't try to make money with it. El 04- Electronics 4 Laboratory Exercise 10 – Parallel Circuits, Part 1 OBJECTIVE: To determine the total resistance of several parallel circuits using one of three formulas for calculations and to estimate the value prior to calculation. The estimation and calculations will be verified with measurements. MATERIALS: Protoboard; multimeter; resistors: 120 , 2.2K, 3.9K, 4.7K(2), 5.1K, 6.8K, 10K, 15K, 18K(4), 33K, 68K(2), 150K. DISCUSSION: Resistors in parallel exhibit multiple current paths to the power supply. As a result, the effective or total resistance that the power supply sees is less than the value of any of the individual resistors. This provides us with some interesting circuitry problems. Fortunately, there are several ways to work with parallel devices easily. Our first rule for parallel resistors, again, is that the total resistance of the circuit will be less than the value of the smallest resistor in the circuit. This is because in a parallel circuit, we have multiple current paths. This allows more current to flow from the power supply than would through the smallest resistor alone. The second rule we can use takes advantage of the fact that resistors typically have tolerances on their values, and may have real values that are as much as 10% above or below the marked value of the device. As a rule of thumb, we can say that any resistor that has a value greater than 20 times the value of the smallest resistor in parallel can be ignored. This is because its value is so high compared to the others that it will have little or no effect on the circuit. This assumes, of course, that we are willing to tolerate some minor error in our design – not all systems would permit this. To illustrate, suppose we have a 1K resistor in parallel with a 22K resistor. The total resistance of the pair is about 956 , which is within the 5% tolerance of a gold-band 1K resistor. So, the 22K resistor can be ignored in most cases. We also have a quick method of estimating the value of two resistors in parallel. For each resistor, divide its value by two. The estimated value of the pair is somewhere between these two half-values. For example, suppose we have a 22K and a 33K in parallel. One-half of 11K is 11K, and one-half of 33K is 16.5K. So, the value of the two devices in parallel can be estimated to be between 11K and 16.5K. A good guess would be 14K, about half-way between the two half-values. The actual value of a 22K and a 33K in parallel is 13.2K, so the 14K guess is pretty close. There are three formulas that we can use to calculate the total resistance of two or more resistors in parallel. The formula you choose depends upon how many devices you have and whether they are of the same or different values. Use the formula that you feel best matches the requirements. Two resistors of equal value: If you have two resistors of equal value in parallel, simply divide the value of one of the resistors by two. The total resistance will be equal to onehalf the resistors’ value. Similarly, if you have three resistors of equal value in parallel, simply divide by 3. Two resistors of unequal value: If you have two resistors of different values in parallel, the easiest approach is to use the product-over-sum formula, RT = (R1 5 R2) / (R1 + R2). Here, the total resistance of the two unequal resistors is equal to the product of the their values divided by the sum of their values. Many resistors of unequal values: In the case where you have more than two resistors of unequal values in parallel, the easiest approach is to use the reciprocal of the sum of the reciprocals formula. This is the same, in effect, as adding up the conductances of the branches of the circuit. This formula appears as 1/RT = 1/R1 + 1/R2 + 1/R3 …, and can be extended to any number of devices. In this exercise, we are given a series of parallel resistor values. For each set of values, we want first to estimate the approximate value of the total resistance of the set. We then will calculate the actual resistance value using an appropriate formula. Finally, we build the circuit and measure the actual value to see how close our estimates and computations have been. PROCEDURE: 1. Examine the chart below. Note that on the left, we have provided sets of resistors that are assumed to be in parallel. We then provide a space where you can note the smallest resistor that is within the set. Next, there is a space for your approximation of the total resistance. Then, we provide a space for the calculated value of the circuit, along with a hint as to which formula to use to make this calculation. Finally, there is space for a measurement. R1 R2 R3 R4 Smallest R Estimate R Formula 4.7K 4.7K ER 6.8K 15K PS 120 3.9K PS 2.2K 68K PS 4.7K 5.1K PS 5.1K 6.8K 150K RS 10K 33K 150K RS Calculated Measure 6.8K 10K 33K RS 18K 18K 18K 18K ER 4.7K 4.7K 68K 68K ER and PS 2. To fill in the chart, follow these steps for each row: A. Examine the values given. B. Select the smallest resistor of the given set, and write its value down in the column marked Smallest R. This may provide you with information when making your estimate. C. Estimate the value of the total resistance of the given resistor set. 1. For two resistors of equal value, simply divide that value by two. For three resistors, divide by three, etc.. 2. For two resistors of unequal value, use the quick method described in the discussion above. 3. For many resistors of unequal value, select the largest and the smallest values. Then. use these with the quick method. D. Next, calculate the actual value of the resistors in parallel. As a hint, we have provided you with a key to the formula that should be used. The key is ER for two resistors (or more) of equal value, PS for product-over-sum, and RS for the reciprocal of the sum of the reciprocals approach. E. Finally, build the circuit and measure the value to see how close your estimate and calculations were to the real value. 3. When you have completed the measurements, return the equipment and supplies to their normal storage areas. Then, answer the questions below in writing for credit. REVIEW QUESTIONS: 1. You are given resistors of the values 1K, 4.7K, 10K, and 20K all in parallel. The total resistance of this group should be smaller than _____________? 2. Six 10K resistors are in parallel. Estimate the total resistance. 3. A 4.7K resistor and a 9.1K resistor are in parallel. Find the total resistance using both the product-over-sum and reciprocal formulas. How do the two computations compare? 4. What must be done to measure the resistance of only one resistor in a parallel circuit? 5. Given a 1K resistor and a 68K resistor in parallel, estimate RT.