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Chapter 19: Q78P (page 803)

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).

Short Answer

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Step by step solution

01

Given data

02

Concept/ Formula used

Kirchhoff's first rule (Junction rule): The sum of all currents entering a junction must equal the sum of all currents leaving the junction.

Kirchhoff's second rule (Loop rule): The algebraic sum of changes in potential around any closed loop must be zero.

03

Current node rule equations

At junction B and E junction rule

I1+I2=I3 ...(i)

Applying voltage rule

For loop ABEFA

−I1R1−I3R2−I1R5+E1=0...(ii)

For loop BCDEB

−E2+I2R3+I2R4+I3R2=0 ...(iii)

For loop ABCDEFA (clockwise)

−I1R1−E2+I2R3+I2R4−I1R5+E1=0...(iv)

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Most popular questions from this chapter

How does the final (equilibrium) charge on the capacitor plates depend on the size of the capacitor plates? On the spacing between the capacitor plates? On the presence of a plastic slab between the plates?

When a particular capacitor, which is initially uncharged, is connected to a battery and a small light bulb, the light bulb is initially bright but gradually gets dimmer, and after 45s it goes out. The diagrams in Figure 19.71 show the electric field in the circuit and the surface charge distribution on the wires at three different times ( 0.01s, 8s, and 240s) after the connection to the bulb is made. Which of the diagrams best represents the state of the circuit at each time specified?

(a)0.01safter the connection is made,

(b)8safter the connection is made,

(c)240safter the connection is made.

The conductivity of tungsten at room temperature,1.8×107A/m2/V/m , is significantly smaller than that of copper. At the very high temperature of a glowing light-bulb filament (nearly 3000 kelvins), the conductivity of tungsten is 18 times smaller than it is at room temperature. The tungsten filament of a thick-filament bulb has a radius of about 0.015 mm. Calculate the electric field required to drive 0.20 A of current through the glowing bulb and show that it is very large compared to the field in the connecting copper wires.

Suppose that you charges a 2.5 Fcapacitor with two 1.5 Vbatteries. How much charge would be on each plate in the final state? How many excess electrons would be on the negative plate?

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 20°to 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.
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