InterviewSolution
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InterviewSolution
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Magnetic flux linked with a stationary loop of resistance `R` varies with respect to time during the time period `T` as follows: `phi=aT(T-r)` Find the amount of heat generated in the loop during that time. Inductance of the coil is negligible.A. `(aT)/(3R)`B. `(a^(2)T^(2))/(3R)`C. `(a^(2)T^(2))`D. `(a^(2)T^92))/(3R)` |
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Answer» Correct Answer - D Given that `phi=at(T-t)` Induced e.m.f., `E=(dphi)/(dt)=(d)/(dt)[at(T-t)]` `=at(0-1)+a(T-t)` `=a(T-2t)` So, induced emf is also a function of time. :. Heat genrated in time `T` is `H=int_(0)^(T)(E^(2))/(R )dt=(a^(2))/(R )int_(0)^(T)(T-at)^(2)dt` `=(a^(2))/(R )int_(0)^(T)(E^(2))/(R )dt=(a^(2))/(R )int_(0)^(T)(T-at)^(2)dt` `=(a^(2))/(R )int_(0)^(T)(T^(2)+4t^(2)-4tT)dt=(a^(2)T(3))/(3R)` |
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