Write an expression for the number of wires of length L_1 cm that (when put in p

Question

Write an expression for the number of wires of length L_1 cm that (when put in parallel) would present the same obstacle as a wire of length L_1. (Call this number of wires, N_1 and give your answer in terms of L and L_1.) Similarly, write an expression for the number of wires of length L cm that (when put in parallel) would present the same obstacle as a w ire of length L_2 (Call this number of wires, N_2 and give your answer in terms of L and L_2) What size of obstacle (called L_eq) is presented when the N_1 + N_2 wires of length L are put in parallel? (Give your answer in terms of L, N_1 and N_2.) Use your previous answers to write your L_eq in terms of L, L_1 and L_2. Then simplity' so that your answer is in terms of L_1 and L_2. Use your generalized expression to calculate the size of the obstacle that is equivalent to the obstacle that results from having L_1 in parallel with L_2. (Include the calculations both for the case L_1 = 31 cm & L_2 = 59 cm and for the case L_1 = 47 cm & L_2 = 61 cm.)

Explanation / Answer

a. N1= L/L1

b. N2=L/L2

c. Leq=L1* L2/(L1+L2)

=L/(N1+N2)

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