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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

Suppose that instead of placing an insulating layer between the plates of the capacitor shown in Figure 19.57, you inserted a metal slab of the same thickness, just barely not touching the plates. In the same circuit, would this capacitor keep the current more nearly constant or less so than capacitor 2 in Question Q4? Explain why this is essentially equivalent to making a capacitor with a shorter distance between the plates.

A circuit consists of a battery, whose emf is K, and five Nichrome wires, three thick and two thin as shown in Figure 19.78. The thicknesses of the wires have been exaggerated in order to give you room to draw inside the wires. The internal resistance of the battery is negligible compared to the resistance of the wires. The voltmeter is not attached until part (e) of the problem. (a) Draw and label appropriately the electric field at the locations marked × inside the wires, paying attention to appropriate relative magnitudes of the vectors that you draw. (b) Show the approximate distribution of charges for this circuit. Make the important aspects of the charge distribution very clear in your drawing, supplementing your diagram if necessary with very brief written descriptions on the diagram. Make sure that parts (a) and (b) of this problem are consistent with each other. (c) Assume that you know the mobile-electron density n and the electron mobility u at room temperature for Nichrome. The lengths(L1,L2,L3)and diameters (d1,d2)of the wires are given on the diagram. Calculate accurately the number of electrons that leave the negative end of the battery every second. Assume that no part of the circuit gets very hot. Express your result in terms of the given quantities(K,L1,L2,L3,d1,d2,nandu) . Explain your work and identify the principles you are using. (d) In the case that d2≪d1, what is the approximate number of electrons that leave the negative end of every second? (e) A voltmeter is attached to the circuit with its + lead connected to location B (halfway along the leftmost thick wire) and its - lead connected to location C (halfway along the leftmost thin wire). In the case that d2≪d1, what is the approximate voltage shown on the voltmeter, including sign? Express your result in terms of the given quantities(K,L1,L2,L3,d1,d2,nandu) .

1/KThe charge on an isolated capacitor does not change when a sheet of glass is inserted between the capacitor plates, and we find that the potential difference decreases (because the electric field inside the insulator is reduced by a factor of 1/K ). Suppose instead that the capacitor is connected to a battery, so that the battery tries to maintain a fixed potential difference across the capacitor. (a) A light bulb and an air-gap capacitor of capacitanceC are connected in series to a battery with known emf. What is the final chargeQ on the positive plate of the capacitor? (b) After fully charging the capacitor, a sheet of plastic whose dielectric constantK is inserted into the capacitor and fills the gap. Does any current run through the light bulb? Why? What is the final charge on the positive plate of the capacitor?

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 net electric field at location A (inside the connecting wire) as a function of time?

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