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CBSE Class 10 Answered

@ wires of resistence a & b of equal mass and same material are taken the diameter of wira a is half of diameter b if the resistence of wire a is24 ohms find the resistence of wire b
Asked by Porwal_kumudini | 16 Jul, 2015, 05:36: PM
answered-by-expert Expert Answer
For wire A:
rA = Radius and lA = length of the wire
For wire B:
rB = Radius and lB = length of the wire
Given that the two wires are made of the saem material and equal masses. Hence, their density (d) and the specific resistance (ρ) is the same.
begin mathsize 12px style πr subscript straight A squared straight l subscript straight A cross times straight d space equals space πr subscript straight B squared straight l subscript straight B cross times space straight d Therefore comma space straight r subscript straight B squared over straight r subscript straight A squared equals straight l subscript straight A over straight l subscript straight B space minus negative negative negative negative left parenthesis Equation space 1 right parenthesis Resistance space of space wire space straight A space is colon straight R subscript straight A equals straight rho straight l subscript straight A over πr subscript straight A squared Resistance space of space wire space straight B space is colon straight R subscript straight B equals straight rho straight l subscript straight B over πr subscript straight B squared Therefore comma space straight R subscript straight A over bold R subscript bold B equals straight r subscript straight B squared over straight r subscript straight A squared cross times straight l subscript straight A over straight l subscript straight B space rightwards arrow straight R subscript straight A over bold R subscript bold B equals straight r subscript straight B to the power of 4 over straight r subscript straight A to the power of 4 space left parenthesis From space equation space 1 right parenthesis But space given space that comma space straight r subscript straight A equals 1 half straight r subscript straight B Therefore comma space straight R subscript straight A over bold R subscript bold B equals 16 Or comma space bold R subscript bold B bold equals 1 over 16 bold R subscript bold A bold rightwards arrow bold space bold R subscript bold B bold equals bold 1 over bold 16 bold cross times bold space bold 24 bold space bold equals bold space bold 1 bold. bold 5 bold space bold capital omega end style
Answered by Yashvanti Jain | 15 Dec, 2017, 07:11: PM

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