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A magnetic flux through a stationary loop with a resistance `R` varies during the time interval `tau` as `phi=at(tau-t)`. Find the amount of the generated in the loop during that timeA. `(aT)/(3R)`B. `(a^(2)T^(2))/(3R)`C. `(a^(2)T^(2))/(R )`D. `(a^(2)T^(3))/(3R)` |
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Answer» Correct Answer - D Given that `phi = at (T-t)` induced emf, `E = (d phi)/(dt) = (d)/(dt)[at(T-t)]` `= at (0-1)+a(T-t) , = a(T-2t)` So, induced emf is alos a function of time. `:.` Heat generated in time `T` is `H = int_(0)^(T)(E^(2))/(R )dt = (a^(2))/(R ) int_(0)^(T)(T-2t)^(2)dt = (a^(2)T^(3))/(3R)` |
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