   Chapter 17, Problem 5CQ

Chapter
Section
Textbook Problem

# Two copper wires A and B have the same length and are connected across the same battery. If RB = 2RA, find (a) the ratio of their cross-sectional areas, Ab/AA, (b) the ratio of their resistivities, ρB/ρA, and (c) the ratio of the currents in each wire, IB/IA.

(a)

To determine
AB:AA , The ratio of cross sectional areas of 2 copper wires A and B of same length.

Explanation

Given Info: The two copper wires A and B have same length and are connected to same battery. RB=2RA

Explanation:

Formula to calculate the area of cross section of wire A is,

AA=ρLRA (I)

• AA is the area of cross section of copper wire A
• ρ is the resistivity of copper
• L is the length of copper wire
• RA is the resistance of copper wire A

Formula to calculate the area of cross section of wire A is,

AB=ρLRB (II)

Divide equation (II) by equation (I),

ABAA=(ρLRB)

(b)

To determine
The ratio of resistivities ρB:ρA

(c)

To determine
The ratio of currents in each wire IB/IA

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