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Circuits - Scenario 4

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SITUATION
​​
A conductor of a certain length and cross-sectional area has a resistance of 10 ohms. If the conductor's length is tripled and ​its ​cross-sectional area​ is doubled, what is its new resistance?


ANALYSIS

1.) Resistivity equation:

Resistance = resistivity constant * (Length / cross-sectional Area)
R = r * (L / A)

​2.) Resistance, old:

R,1 = r * (L,1 / A,1)
R,1 = 10 ohms
10 = r * (L,1 / A,1)

​3.) Parameters changed:​

​L,2 = 3 L,1
A,2 = 2 A,1
​
​4.) Resistance, new:

R,2 = r * (L,2 / A,2)
R,2 = r * ​[ ​(3​ ​L,1​)​ / ​(​2​ ​A,1)
R,2 = [ r * (L,1 / A,1) ] * 1.5
R,2 = 10 * 1.5
R,2 = 15​ ohms​

CONCLUSION

​With the conductor's length tripled and cross-sectional area doubled​, the conductor's resistance becomes 15 ohms.​ Resistance is directly proportional to length and inversely proportional to​ cross-sectional area, according to the resistivity equation.

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