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Chapter 19: Q25Q (page 796)

State whether the following statement is true or false, and briefly explain why: “In 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.”

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

The capacitor in Figure 19.68 is initially uncharged, then the circuit is connected. Which graph in Figure 19.66 best describes the magnitude of the fringe field of the capacitor at location A(inside the connecting wire) as a function of time?

How is the charging time for a capacitor correlated with the initial current? That is, if the initial current is bigger, is the charging time, longer, shorter, or the same?

The capacitor in Figure 19.67 is initially uncharged, then the circuit is connected. Which graph in Figure 19.66 best describes the current through the bulb as a function of time?

(a) If the current through a battery is doubled, by what factor is the battery power increased? (b) If the current through a resistor is doubled, by what factor is the power dissipation increased? (c) Explain why these factors are the same or different (depending on what you find).

A circuit consists of two batteries (with negligible resistance), six ohmic resistors and connecting wires that have negligible resistance. The resistance R1is 10Ω, R2 is 20Ω, R3 is 30Ω, R4is 12Ω, R5is 15Ω and R6 is 20Ω. Unknown currents I1,I2 ,I3 ,I4 , I5 and I6 have their directions marked on the circuit diagram in figure 19.87.

(a) Write down a set of equations that could be solved for the six unknown currents. Make sure you can explain how to you got these equations. (b) When a correct set of equations is solved the currents are as follows (to the nearest miiampeares) I1=0.4394A, I2=0.3312A, I3=0.0065A, I4=0.1082A, I5=0.3247Aand I6=0.4329A. Check your equations by substituting in these numbers. (c) Suppose that you connect the negative lead of a voltmeter to location C. What does the voltmeter read, including both magnitude and sign? (d) What does the power output of the 5 V battery? (e) Resistor is made of a very thin metal wire that is 3 mm long, with a diameter of 0.1 mm. What is the electric field inside the metal resistor.
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