Quiz
Q1) You have three 100 resistors available. How would you connect these three resistors to produce a 150 equivalent resistance? You must use all of the resistors.
A. Connect all three resistors in parallel.
B. Connect all three resistors in series.
C. Connect one resistor in series with two resistors in parallel.
D. Connect two resistors in series with the third resistor in parallel to the first two.
Answer) C.
Q2) A circuit is constructed as follows: four resistors in parallel connected in series with three resistors in parallel connected in series with two resistors in parallel. All of the resistors have the same value. How does the equivalent resistance of this circuit compare to the resistance of a single resistor?
A. The equivalent resistance is less than a single resistor.
B. The equivalent resistance is the same as a single resistor.
C. The equivalent resistance is greater than a single resistor.
D. The equivalent resistance cannot be determined without the resistance value of a single resistor.
Answer) C.
A. The equivalent resistance is less than a single resistor.
B. The equivalent resistance is the same as a single resistor.
C. The equivalent resistance is greater than a single resistor.
D. The equivalent resistance cannot be determined without the resistance value of a single resistor.
Answer) C.
Resistors in parallel total resistance Simulation
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RESISTORS COMBINED BOTH IN PARALLEL AND IN SERIES
Series and parallel circuits are not often encountered independent of one another. Most circuits today employ both series and parallel wiring to utilize the advantages of each type.
A common example of a complex circuit is the electrical wiring typical in a home. In a home, a fuse or circuit breaker is connected in series to numerous outlets, which are wired to one another in parallel. An example of a typical household circuit is shown in Figure 1.
Figure 1. (a) When all of these devices are plugged into the same household circuit, (b) the result is a parallel combination of resistors in series with a circuit breaker.
As a result of the outlets being wired in parallel, all the appliances operate independently; if one is switched off, any others remain on.Wiring the outlets in parallel ensures that an identical potential difference exists across any appliance.
This way, appliance manufacturers can produce appliances that all use the same standard potential difference.
To prevent excessive current, a fuse or circuit breaker must be placed in series with all of the outlets. Fuses and circuit breakers open the circuit when the current becomes too high. A fuse is a small metallic strip that melts if the current exceeds a certain value. After a fuse has melted, it must be replaced. A circuit breaker, a more modern device, triggers a switch when current reaches a certain value. The switch must be reset, rather than replaced, after the circuit overload has been removed. Both fuses and circuit breakers must be in series with the entire load to prevent excessive current from reaching any appliance. In fact, if all the devices in Figure 1 were used at once, the circuit would be overloaded. The circuit breaker would interrupt the current.
Fuses and circuit breakers are carefully selected to meet the demands of a circuit. If the circuit is to carry currents as large as 30 A, an appropriate fuse or circuit breaker must be used. Because the fuse or circuit breaker is placed in series with the rest of the circuit, the current in the fuse or circuit breaker is the same as the total current in the circuit. To find this current, one must determine the equivalent resistance.
When determining the equivalent resistance for a complex circuit, you must simplify the circuit into groups of series and parallel resistors and then find the equivalent resistance for each group by using the rules for finding the equivalent resistance of series and parallel resistors.
Work backward to find the current in and potential difference across a part of a circuit Now that the equivalent resistance for a complex circuit has been determined, you can work backward to find the current in and potential difference across any resistor in that circuit. In the household example, substitute potential difference and equivalent resistance in $\Delta V = IR$ to find the total current in the circuit. Because the fuse or circuit breaker is in series with the load, the current in it is equal to the total current. Once this total current is determined, $\Delta V = IR$ can again be used to find the potential difference across the fuse or circuit breaker.
There is no single formula for finding the current in and potential difference across a resistor buried inside a complex circuit. Instead, $\Delta V = IR$ and the rules reviewed in Table must be applied to smaller pieces of the circuit until the desired values are found.
