### Circuits - Scenario 4

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.