   Chapter 17, Problem 68AP

Chapter
Section
Textbook Problem

A man wishes to vacuum his car with a canister vacuum cleaner marked 535 W at 120. V. The car is parked far from the building, so he uses an extension cord 15.0 m long to plug the cleaner into a 120.-V source. Assume the cleaner has constant resistance. (a) If the resistance of each of the two conductors of the extension cord is 0.900 Ω, what is the actual power delivered to the cleaner? (b) If, instead, the power is to be at least 525 W, what must be the diameter of each of two identical copper conductors in the cord the young man buys? (c) Repeat part (b) if the power is to be at least 532 W. Suggestion: A symbolic solution can simplify the calculations.

(a)

To determine
The actual power delivered to vacuum cleaner.

Explanation

Given Info: A vacuum cleaner utilizes 535W power when connected to 120V supply. The extension cord from vacuum cleaner which used to clean the car consists of two conducting wires. The total length of extension cord is 15.0m . The resistance of each conductor is 0.900Ω .

Explanation:

Formula to calculate the total current in the circuit is,

I=ΔVRtotal (I)

• I is the current in the circuit,
• ΔV is the voltage of power supply,
• Rtotal is the total resistance in the path of current,

Formula to calculate the total resistance in the path of current is,

Rtotal=Rvaccum+2Rc (II)

• Rvaccum is the resistance offered by the vacuum cleaner,
• Rc is the resistance offered by each conductor in the extension cord,

Formula to calculate the resistance offered by vacuum cleaner is,

Rvaccum=(ΔV)2P (III)

• P is the rated power of vacuum cleaner,

Substitute equation (III) in equation (II) and rewrite equation (II).

Rtotal=(ΔV)2P+2Rc (IV)

Substitute equation (IV) in equation (I) and rewrite equation (I).

I=ΔV((ΔV)2P+2Rc)

Substitute 120V for ΔV , 535W for P and 0.900Ω for Rc in the above equation to find I .

I=120V(((120V)2535W)+2(0

(b)

To determine
The diameter of each of identical copper wire in the extension cord when minimum power is 525W .

(c)

To determine
The diameter of each of identical copper wire in the extension cord when minimum power is 532W .

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