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A rod of length L and cross-section area A lies along the x-axis between x=0 and x=L. The material obeys Ohm's law and its resistivity varies along the rod according to rho left parenthesis x right parenthesis equals rho subscript 0 end subscript e to the power of negative x divided by L end exponent. Find the total resistance of the rod. The end of the rod at x=0 is at a potential V subscript 0 end subscript and it is zero at x=L.

  1. fraction numerator rho subscript 0 end subscript L over denominator A end fraction open parentheses fraction numerator 1 over denominator e end fraction close parentheses    
  2. fraction numerator rho subscript 0 end subscript L over denominator A end fraction left parenthesis e right parenthesis    
  3. fraction numerator rho subscript 0 end subscript L over denominator A end fraction open parentheses 1 minus fraction numerator 1 over denominator e end fraction close parentheses    
  4. fraction numerator rho subscript 0 end subscript L over denominator A end fraction left parenthesis e minus 1 right parenthesis    

The correct answer is: fraction numerator rho subscript 0 end subscript L over denominator A end fraction open parentheses 1 minus fraction numerator 1 over denominator e end fraction close parentheses

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