1.

The current i amperes at any time t is given by (L frac{di}{dt} + Ri = E ), when a resistance R ohms is connected in series with an inductance L henries and E.M.F of E volts. If E=10 sin(t) volts and i=0 when t=0,which among the following is the correct expression for i(t) at any time t?

A. ( frac{10}{R^2+L^2} (R cos u2061t L sin u2061t + Le^{ frac{Rt}{L}}) )
B. ( frac{10}{R^2+L^2} (R sin u2061t + L cos u2061t Le^{ frac{Rt}{L}}) )
C. ( frac{10}{R^2+L^2} (R sin u2061t L cos u2061t + Le^{ frac{-Rt}{L}}) )
D. ( frac{10}{R^2+L^2} (L cos u2061t R sin u2061t + Le^{ frac{-Rt}{L}}) )
Answer» D. ( frac{10}{R^2+L^2} (L cos u2061t R sin u2061t + Le^{ frac{-Rt}{L}}) )


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