Assignment 8- Fundamentals of Circuits

# Assignment 8- Fundamentals of Circuits - Resistors in...

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Resistors in Parallel A circuit contains a source of constant voltage and two resistors connected in parallel, as shown in the figure. Resistor 1 has resistance , and resistor 2 has resistance . Part A Which two of the following statements are true? 1. The voltage source provides a constant voltage, a part of which, , drops off across resistor 1, and the remainder, , across resistor 2. Hence . 2. The voltage drops across resistor 1 and across resistor 2 are the same, and they are independent of the values of and . Both and are equal to the voltage provided by the source. Hence .

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Picture 23 Picture 24 Picture 25 Picture 26 Resistors in Parallel Part A 3. The current provided by the voltage source splits: A part of it, , flows through resistor 1, while the remainder, , flows through resistor 2. Hence . 4. The currents through resistor 1 and through resistor 2 are the same, and they are equal to the current provided by the source. Hence . ANSWER: 1 and 3 1 and 4 2 and 3 2 and 4 Correct Part B To simplify the circuit diagram, we represent the two resistances and by just one resistance, , as shown in the figure.
Resistors in Parallel Part A What is the value of ? Note that this new resistor is equivalent to the combination of resistors 1 and 2 in parallel in the sense that if you replaced one by the other, the electrical properties of the circuit would remain unchanged. Hint B.1 Hint not displayed Express the resistance in terms of and . ANSWER: = Correct Part C Now consider three resistors in parallel, with resistances , , and , as shown in the figure.

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Resistors in Parallel Part C Again, draw a circuit diagram with a single equivalent resistor, with resistance . What is the value of ? Hint C.1 Method 1: Use current relationships and Ohm's law Hint not displayed Hint C.2 Method 2: Generalize and extend the previous result Hint not displayed Express your answer in terms of , , and . ANSWER: = Correct
Resistors in Parallel Part C You have calculated two specific cases of the law for addition of resistances in parallel. Using the principle of mathematical induction, one can show that if resistors of resistances are connected in parallel, they are equivalent to a single resistor of resistance , where .

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Brightness of Light Bulbs Consider a circuit containing five identical lightbulbs and an ideal battery. Part A Rank the brightness of the five bulbs (A through E) from brightest to dimmest. (The more current flowing through a bulb, the brighter it will be.) Hint A.1 Comparing bulb A to bulb B Hint not displayed Hint A.2 Comparing bulb D to bulb E Hint not displayed Hint A.3 Comparing bulb C to bulb D or E Hint not displayed Hint A.4 Comparing bulb C to bulb A or B Hint not displayed List the bulbs in order from brightest to dimmest. Between each pair of bulbs, use the symbol > to indicate that the left-hand bulb is brighter than the right-hand bulb, or = to indicate that the bulbs have the same brightness. For example, "B=C=E>A>D" means that bulbs B, C, and E all have the same
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Assignment 8- Fundamentals of Circuits - Resistors in...

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