General Science
10th Physics - Resistance Factors
If the length of a uniform conducting wire is doubled and its cross-sectional area is halved, its electrical resistance will become:
यदि किसी चालक तार की लंबाई दोगुनी कर दी जाए और उसका अनुप्रस्थ काट क्षेत्रफल आधा कर दिया जाए, तो उसका नया प्रतिरोध कितना हो जाएगा?
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Official Solution & Conceptual Rationale
Class 10 NCERT Science - Chapter 12
Resistance R = ρ(L / A). If L is doubled (2L) and A is halved (A/2), new resistance R' = ρ(2L / (A/2)) = 4 · (ρL/A) = 4R.
R = ρ (L / A)। नई लंबाई L' = 2L, नया क्षेत्रफल A' = A/2। अतः R' = ρ (2L / (A/2)) = 4 × (ρL/A) = 4R।