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State whether the following statement is true or false, and briefly explain why: 鈥淚n the two circuits shown in Figure 19.64, the battery output power is greater in circuit 2 because there is an additional resistor dissipating power.鈥

Short Answer

Expert verified

The statement is false since output power is inversely proportional to the total resistance of the circuit.

Step by step solution

01

Given data

A 10Vbattery is connected first to a resistance R1 (circuit 1) and then to a series connection of R1 and R2 (circuit 2).

The following statement is provided:

In the two circuits shown in Figure 19.64, the battery output power is greater in circuit 2 because there is an additional resistor R2 dissipating power.

02

Dissipated power

The power dissipated in a circuit of net EMF and total resistance is

P=E2R .....(i)

03

Determination of whether the provided statement is true is false

From equation (1), the total output power in circuit 1 is:

P1=100V2R1

The equivalent resistance of circuit 2 is R1+R2. Thus, from equation (1), the total output power in circuit 2 is:

P2=100V2R1+R2

Evidently, P2>P1.

Thus, the statement is false.

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Most popular questions from this chapter

Question: in circuit 1 (Figure 19.72), an uncharged capacitor is connected in series with two batteries and one light bulb. Circuit 2 (Figure 19.72) contains two light bulbs identical to the bulb in the circuit; in all other respects, it is identical to circuit 1. In circuit 1, the light bulb stays lit for 25 s. The following questions refer to these circuits. You should draw diagrams representing the fields and charges in each circuit at the times mentioned, in order to answer the questions.

(a)One microsecond after connecting both circuits, which of the following are true? Chose all that apply: (1) the net electric field at location B in circuit 1 is larger than the net electric field at location B in circuit 2. (2) At location A in 1, electrons flow to the left. (3) At location A in circuit 1, the electric fields due to charges on the surface of the wires and batteries points to the right. (4) in circuit 1 the potential difference across the capacitor plates is equal to the emf of the batteries. (5) The current in circuit 1 is larger than the current in circuit 2.

(b)Two seconds after connecting both circuits, which of the following are true? Choose all that apply: (1) there is more charge on the plates of capacitor 1 than there is on the plates of capacitor 2. (2) there is negative charge on the right plate of the capacitor in circuit 1. (3) At location B in circuit 2 the net electric field points to the right. (4) At location B in circuit 2 the fringe field of the capacitor points to the right. (5) At location A in circuit 1 the fringe field of the capacitor points to the left.

(c)Which of the graphs in Figure 19.73 represents the amount of charge on the positive plate of the capacitor in circuit 1 as a function of time?

(d)Which of the graphs in Figure 19.73 represents the current in circuit 1 as a function of time?

A particular capacitor is initially charged. Then a high-resistance Nichrome wire is connected between the plates of the capacitor, as shown in Figure 19.69. The needle of a compass placed under the wire deflects 20to the east as soon as the connection is made. After 60sthe compass needle no longer deflects.

(a)Which of the diagrams in Figure 19.69 best indicates the electron current at three locations in this circuit? (1) 0.01safter the circuit is connected, (2) 15s after the circuit is connected, (3) 120s after the circuit is connected.

(b)Which of the diagrams in Figure 19.70 best indicates the net electric field inside the wire at three locations in this circuit? (1) 0.01s after the circuit is connected, (2) 15safter the circuit is connected, (3) 120s after the circuit is connected.

Someone said, 鈥淐urrent takes the path of least resistance.鈥 What鈥檚 wrong with this statement?

Which of the following are ohmic resistors? For those that aren鈥檛, briefly state why they aren鈥檛. (a) Nichrome wire, (b) a thin filament light bulb, (c) a plastic rod, (d) salt water, (e) silicon (a semiconductor)

In the circuit shown in Figure 19.77 the emf of the battery is 7.4V. Resistor R1has a resistance of 31, resistor R2 has a resistance of 47, and resistor R3has a resistance of 52 . A steady current flows through the circuit.

(a)What is the equivalent resistance of R1and R2 ? (b) What is the equivalent resistance of all three resistors? (c) What is the conventional current throughR3

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