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Chapter 19: Q56P-b (page 799)

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

Short Answer

Expert verified

70.68惟

Step by step solution

01

Given Data

R1=31惟R2=47惟R3=52惟emf=7.4V

02

Concept

The equivalent resistance is the addition of the resistances, when the batteries are connected in series.

03

Step 3(b): Determine the equivalent resistance of all three resistors

The equivalent resistance of all the three resistors,

R=R3+R4=52+18.68=70.68惟Referring to subpartaof the SID:875865 - 19 - 56P - a,takeR4value

Hence, the equivalent resistance of all three resistors is 70.68惟

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Most popular questions from this chapter

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 脳 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鈮�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鈮�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).

For the circuit shown in figure 19.86, which consists of batteries with known emf and ohmic resistors with known resistance, write the correct number of energy-conservation and current node rule equations that would be adequate to solve for the unknown currents, but do not solve the equations. Label nodes and currents on the diagram, and identify each equation (energy or current, and for which loop or node).

Consider a copper wire with a cross-sectional area of 1 mm2 (similar to your connecting wires ) and carrying 0.3 A of current, which is about what you get in a circuit with a thick-filament bulb and two batteries in series. Calculate the strength of the very small electric field required to drive this current through the wire.

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

The insulating layer between the plates of a capacitor not only holds the plates apart to prevent conducting contact but also has a big effect on charging. Consider two capacitors whose only difference is that capacitor number has nothing between the plates, while capacitor number has a layer of plastic in the gap (Figure 19.57). They are placed in two different circuits having similar batteries and bulbs in series with the capacitor.

Show that in the first fraction of a second the current stays more nearly constant (decreases less rapidly) in the circuit with capacitor number . Explain your reasoning in detail. Hint: Consider the electric fields produced in the nearby wires by this plastic-filled capacitor. Suppose that the plastic is replaced by a different plastic that polarizes more easily. In the same circuit, would this capacitor keep the current more nearly constant or less so than capacitor ?

A more extensive analysis shows that this trend holds true for the entire charging process: the capacitor containing an easily polarized insulator ends up with more charge on its plates. The capacitor you have been using is filled with an insulator that polarizes extremely easily.
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