Resistance of resistor

Electricity and Magnetism Level 1

R 1 R_1 and R 2 R_2 in the above figure are two resistors made of the same material. Their respective cross sectional areas and lengths are ( 3 S , L ) (3S, L) and ( S , 2 L ) . (S, 2L). If the resistance of R 1 R_1 is 10.0 Ω , 10.0 \ \Omega, then what is the resistance of R 2 ? R_2?

10.0 Ω 10.0 \ \Omega 30.0 Ω 30.0 \ \Omega 6.0 Ω 6.0 \ \Omega 60.0 Ω 60.0 \ \Omega

Lakshan Dumpa by Lakshan Dumpa , 24, India

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2 solutions

Chew-Seong Cheong
Jan 17, 2015

Resistance is directly proportional the length and inversely proportional to the cross-sectional area: R ∝ l A R \propto \dfrac {l} {A}

Therefore, R 2 R 1 = l 2 A 1 l 1 A 2 = 2 L ( 3 S ) L S = 6 ⇒ R 2 = 6 R 1 = 6 × 10 = 60 Ω \dfrac {R_2}{R_1} = \dfrac {l_2A_1} {l_1A_2} = \dfrac {2L(3S)}{LS} = 6 \quad \Rightarrow R_2 = 6 R_1 = 6 \times 10 = \boxed{60}\space \Omega

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Good except 6x10ohms is 60 ohms just the written solution.

Dylan Scupin-Dursema - 6 years, 2 months ago
Masood Salik
Aug 24, 2014

R=roh*L/A wher roh = resistivity L= length A= area

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