a. Make a new resistor of length 2l and diameter 2d b. Connect two of the origin

Question

a. Make a new resistor of length 2l and diameter 2d

b. Connect two of the original resistors in series

c. connect three of the original resistors in series

d. connect two the orginal resistors in parallel

e. connect three of the original resistors in parallel

a. Make a new resistor of length 2l and diameter 2d

b. Connect two of the original resistors in series

c. connect three of the original resistors in series

d. connect two the orginal resistors in parallel

e. connect three of the original resistors in parallel

Explanation / Answer

a.the original resistance of the resistor is R = ( * l/A) = ( * l/ * (d2/4)) =(4 * l/ * d2) ---------(1) when l1 = 2l and d1 = 2d then wehave R1 = ( * 2l/ *(d12/4)) = ( * 2l/ *((2d)2/4)) = (2 * l/ * d2)----------(2) (2)/(1) (R1/R) = [(2 * l/ *d2)/(4 * l/ * d2)] = (1/2) or R1 = (R/2) b.when two of the original resistors are connected in serieswe have Req = R + R = 2R c.when three of the original resistors are connected in serieswe have Req = R + R + R = 3R d.when two of the original resistors are connectedin parallel we have (1/Req) = (1/R) + (1/R) = (1 + 1/R) = (2/R) or Req = (R/2) e.when three of the original resistors are connectedin parallel we have (1/Req) = (1/R) + (1/R) + (1/R) = (1 + 1 + 1/R) = (3/R) or Req = (R/3) therefore,the largest resistance is produced when three of theoriginal resistors are connected in series. Req = R + R + R = 3R d.when two of the original resistors are connectedin parallel we have (1/Req) = (1/R) + (1/R) = (1 + 1/R) = (2/R) or Req = (R/2) e.when three of the original resistors are connectedin parallel we have (1/Req) = (1/R) + (1/R) + (1/R) = (1 + 1 + 1/R) = (3/R) or Req = (R/3) therefore,the largest resistance is produced when three of theoriginal resistors are connected in series.

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