Question

1-What is the resistance of a 5km long copper wire with a diameter of 4mm?

a. 1.65 ohms

b. 0.0015 ohms

c. .0065 ohms

d. 6.7 ohms

2- three 4mF capacitor are connected in series across a 12 V battery. The total charges stored by this compination of capacitor is

A. 24 mC

B. 16 mC

C. 48 mC

D. 144 mC

E. None of the above

3. What would be the energy stored in the capacitor in the previous question?

A. 144 mJ

B. 288 mJ

C. 864 mJ

D. 96 mJ

E. None above

Answer 1

1.

   Given lengthof the copper wire l = 5 km = 5*10^3 m,

   resistivity of copper is rho = 1.68*10^-8 ohm m

   diameter of the wire is d= 4mm, r = 2mm= 2*10^-3 m

from the relation between R, rho,A,l i

       R = rho*l/A
       R = (1.68*10^-8*5*10^3)/(pi(2*10^-3)^2) ohm

       R = 6.6845076098596 ohm = 6.7 ohm
answer is option d---------------------> Answer

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2.
    capacitance of each capacitor C = 4 mF = 4*10^-3 F, battery of V = 12 V

   three capacitors are connected in series then net capacitance is Cn = C/3 = 4*10^-3 /3 =1.33 mF

from the relation Q = C*V ==> Q = 1.33*10^-3*12 C = 15.96 mC = 16 mC ------------>> anaswer --B

3

   energy stored in the capacitor is U = 1/2 c* v^2 = 0.5*1.33*10^-3*12^2 J

  
           U = 0.09576 J
           U = 95.76 mJ
           U = 96 mJ <<<-------------- answer --D