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Chapter 25: Problem 6

Which of the arrangements of three identical light bulbs shown in the figure draws most current from the battery? a) \(A\) d) All three draw equal current. b) \(B\) e) \(\mathrm{A}\) and \(\mathrm{C}\) are tied for drawing the most current. c) \(C\)

Short Answer

Expert verified
Answer: a) Three light bulbs connected in parallel.

Step by step solution

01

Identify type of connections in arrangements A, B, and C

In arrangement A, the three light bulbs are connected in parallel. In arrangement B, the light bulbs are connected in series. In arrangement C, one light bulb is connected in parallel to two others that are connected in series.
02

Calculate the total resistance of each arrangement

Let R be the resistance of a single lightbulb. For arrangement A, since all light bulbs are in parallel, the reciprocal of the total resistance is found by summing the reciprocals of individual resistances: \(\frac{1}{R_A} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R}\). For arrangement B, since all light bulbs are in series, the total resistance is found by summing the individual resistances: \(R_B = R + R + R\). For arrangement C, note that two light bulbs are connected in series and their total resistance is \(R + R\), which is then connected in parallel to another lightbulb, thus we have: \(\frac{1}{R_C} = \frac{1}{R} + \frac{1}{R+R}\).
03

Use Ohm's Law to find the current drawn in each arrangement

Ohm's Law states that \(I = \frac{V}{R}\). To compare the current drawn by each arrangement, we can calculate their currents using the total resistance calculated in the previous step: For arrangement A: \(I_A = \frac{V}{R_A}\). For arrangement B: \(I_B = \frac{V}{R_B}\). For arrangement C: \(I_C = \frac{V}{R_C}\).
04

Compare the currents drawn by each arrangement

By observing the total resistance calculations in each arrangement, we can see that arrangement A has a smaller total resistance compared to the other arrangements. Since the current is inversely proportional to the resistance, according to Ohm's law, a smaller resistance will result in a higher current. Thus, arrangement A draws the most current from the battery. The correct answer is a) A.

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Most popular questions from this chapter

Two conductors are made of the same material and have the same length \(L\). Conductor \(\mathrm{A}\) is a hollow tube with inside diameter \(2.00 \mathrm{~mm}\) and outside diameter \(3.00 \mathrm{~mm} ;\) conductor \(\mathrm{B}\) is a solid wire with radius \(R_{\mathrm{B}}\). What value of \(R_{\mathrm{B}}\) is required for the two conductors to have the same resistance measured between their ends?

Before bendable tungsten filaments were developed, Thomas Edison used carbon filaments in his light bulbs. Though carbon has a very high melting temperature \(\left(3599^{\circ} \mathrm{C}\right)\) its sublimation rate is high at high temperatures. So carbonfilament bulbs were kept at lower temperatures, thereby rendering them dimmer than later tungsten-based bulbs. A typical carbon-filament bulb requires an average power of \(40 \mathrm{~W}\), when 110 volts is applied across it, and has a filament temperature of \(1800^{\circ} \mathrm{C}\). Carbon, unlike copper, has a negative temperature coefficient of resistivity: \(\alpha=-0.0005^{\circ} \mathrm{C}^{-1}\) Calculate the resistance at room temperature \(\left(20^{\circ} \mathrm{C}\right)\) of this carbon filament.

Two resistors with resistances \(R_{1}\) and \(R_{2}\) are connected in parallel. Demonstrate that, no matter what the actual values of \(R_{1}\) and \(R_{2}\) are, the equivalent resistance is always less than the smaller of the two resistances.

Three resistors are connected to a power supply with \(V=110 . \mathrm{V}\) as shown in the figure a) Find the potential drop across \(R_{3}\) b) Find the current in \(R_{1}\). c) Find the rate at which thermal energy is dissipated from \(R_{2}\).

A light bulb is connected to a source of emf. There is a \(6.20 \mathrm{~V}\) drop across the light bulb, and a current of 4.1 A flowing through the light bulb. a) What is the resistance of the light bulb? b) A second light bulb, identical to the first, is connected in series with the first bulb. The potential drop across the bulbs is now \(6.29 \mathrm{~V},\) and the current through the bulbs is \(2.9 \mathrm{~A}\). Calculate the resistance of each light bulb. c) Why are your answers to parts (a) and (b) not the same?
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