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An inductor with an inductance of 2.10 H and a resistance of 7.50 ohm is connect

ID: 2078005 • Letter: A

Question

An inductor with an inductance of 2.10 H and a resistance of 7.50 ohm is connected to the terminals of a battery with an emf of 6.50 V and negligible internal resistance. You may want to review For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Analyzing an r-l circuit. elementof - iR - L di/dt = 0 so i = elementof/R (1 - e^(-R/L)t). Initially (t = 0), i = 0 so elementof - L di/dt = 0 di/dt = elementof/L = 6.50 V/2.10 H = 3.10 A/s Find the rate of increase of current at the instant when the current is 0.500 A.

Explanation / Answer

(a)    battery voltage = initialrate * inductance .

         6.50 = initial rate * 2.10 .

   initial rate = 3.10 A/s.

(b)     rate of current increase = initial rate *e-t/T      where   T = L/R = 2.1/7.5 = 0.28.

also...     current = (V/R) (1 - e-t/T )     so....

            e-t/T =  1 - (current* R / V) = 1 - 0.500 * 7.5 / 6.5 =    0.423.

    rate of current inc = 3.10* 0.423 = 1.312 A/s