A platinum wire of diameter 2.9 mm is connected in series to a 50 F capacitor an

Question

A platinum wire of diameter 2.9 mm is connected in series to a 50 F capacitor and a 0.00068 H inductor to form an RLC circuit. The resistivity of platinum is 1.1 × 107 · m. Calculate the length of the platinum wire when the current is critically damped. An- swer in units of m. A platinum wire of diameter 2.9 mm is connected in series to a 50 F capacitor and a 0.00068 H inductor to form an RLC circuit. The resistivity of platinum is 1.1 × 107 · m. Calculate the length of the platinum wire when the current is critically damped. An- swer in units of m.

Explanation / Answer

Given :
                      Diameter of the platinum wire (d) = 2.9 mm                                                                  = 2.9 x 10-3   m Capacitance is : C = 50 F                              = 50 x 10-6    F Inductance is :                     L = 0.00068 x 10-6  H Under critically damped condition the resistance becomes:        R = Rc       = (4 L / C)        = (4*  0.00068 x 10-6 )/ 50 x 10-6           =   0.007375          We know that :    R = l / A    Length of the wire is :              l = R A /                 = (0.007375 * (1.45 x10-3 m)2 / 1.1 ×107 · m.                 = ---------- m    solve for the length of the wire . Hope this helps u!

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