In each of the accompanying figures the voltage across and the current through e

Question

In each of the accompanying figures the voltage across and the current through each resistor are given Determine the resistor indicated The resistance of a wire of uniform material and of constant cross sectional area is given by the equation R = rho L_i A where rho = resistivity (depends on material and slightly, on temperature) L = length of the wire A = cross sectional area of the wire. A certain wire of cross sectional area A and length L has a resistance of 250 Ohm. For each of the possible changes it indicated below, determine the new resistance of the wire Length of wire made 2 L Length of wire made (1/5) L Cross sectional area tripled cross sectional area made (1/4) its original values Length of wire made 3L and cross section doubled wire circular in cross section and diameter doubled

Explanation / Answer

3) To ..from left to right

1) R = V/I = (20/3)+-(2/0.5) = 6.67+-4

2) R = V/I = 6/24 = 0.25 ohm

Bottom from left to right

3) R = V/I = 0.8/0.6 = 1.33 ohm

4) Total R = (V/I)+R = (18/2)+30 = 9+30 = 39 ohm

4) Here, for R = p * L/A

Now, for the changes

a) as length is doubled , resistance is directly proporational to Length

Rnew = 2 * R = 2 * 250 = 500 Ohm

Rnew = 500 Ohm

b)

length is 1/5 times , resistance is directly proporational to Length

Rnew = 250/5 = 50 Ohm

c)

Area is tripled , as resitance is inversely proporational to area

R = 250/3 = 83.33 Ohm

d)

Area is 1/4 times , as resitance is inversely proporational to area

R = 250 * 4 = 1000 Ohm

e)

NOw, for the new wire

Rnew = 3 * R/2 = 1.5 * 250

Rnew = 375 Ohm

f) as diameter is doubled , A = pi * d^2/4

area will be 4 times

Rnew = 250/4 = 62.5 Ohm

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