The magnetic flux linked with a closed coil of resistance 10 varies with time t according to the equation = 3t^2 + 2t + 1 , where is in Weber and t is in seconds. The net charge that flows through the coil during the time interval from t=0 to t=2 s is:

Step-by-step solution

The net charge Q that flows through a coil of resistance R due to a change in magnetic flux is given by the relation: Q = R Given the flux equation: (t) = 3t^2 + 2t + 1 Calculate the initial flux at t=0 : (0) = 3(0)^2 + 2(0) + 1 = 1 Wb Calculate the final flux at t=2 s : (2) = 3(2)^2 + 2(2) + 1 = 12 + 4 + 1 = 17 Wb The change in magnetic flux is: = (2) - (0) = 17 - 1 = 16 Wb Now, substituting the values into the charge equation: Q = 16 10 = 1.6 C Answer: 1.6 C