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, 17:36: PM
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](https://images.topperlearning.com/topper/tinymce/cache/1b1a968aa414507c921bccd18fb63580.png)
Answered by Yashvanti Jain | 15 Dec, 2017, 19:11: PM
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