vi)A metallic wire of length \( L \) and cross sectional area \( A \) has a resistance \( R \). Two wires of same material,length \( L / 2 \) and cross sectional area \( 3 A \) are connected in series. The combination has resistance of a) \( R / 6 \) b) R/3 c) \( 3 R \) d) \( 6 R \)
vi)A metallic wire of length \( L \) and cross sectional area \( A \) has a resistance \( R \). Two wires of same material,length \( L / 2 \) and cross sectional area \( 3 A \) are connected in series. The combination has resistance of a) \( R / 6 \) b) R/3 c) \( 3 R \) d) \( 6 R \)
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3 Answers
Given R1 = R
l1 = L
A1 = A
l2 = L/2
A2 = 3A
A2 = ?
We know that,
The resistance of the wire R = ρl/A
ρ1 = ρ2 = ρ same metallic wire
R2 = ρl2/A2 ...(1)
R1 = ρl1/A1 ...(2)
Divided equation R2/R1
R2/R1 = ρl2/A2 x A1/ρl1
(∵ R1 = R, l2 = L/2 and A2 = 3A)
R2/R = \(\frac{L/2}{3A}\) x A/L
R2/R = 1/6
R2 = R/6
option (a) is correct.
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Answered