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?

Question

TuteeHUB · Accepted Answer

$\frac{10}{R^2+L^2} (L cos⁡t – R sin⁡t + Le^{\frac{-Rt}{L}})$

TuteeHUB · Answer

$\frac{10}{R^2+L^2} (R cos⁡t – L sin⁡t + Le^{\frac{Rt}{L}})$

TuteeHUB · Answer

$\frac{10}{R^2+L^2} (R sin⁡t + L cos⁡t – Le^{\frac{Rt}{L}})$

TuteeHUB · Answer

$\frac{10}{R^2+L^2} (R sin⁡t – L cos⁡t + Le^{\frac{-Rt}{L}})$

TuteeHUB · Answer

$\frac{10}{R^2+L^2} (L cos⁡t – R sin⁡t + Le^{\frac{-Rt}{L}})$

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.	\(\frac{10}{R^2+L^2} (R cos⁡t – L sin⁡t + Le^{\frac{Rt}{L}})\)
B.	\(\frac{10}{R^2+L^2} (R sin⁡t + L cos⁡t – Le^{\frac{Rt}{L}})\)
C.	\(\frac{10}{R^2+L^2} (R sin⁡t – L cos⁡t + Le^{\frac{-Rt}{L}})\)
D.	\(\frac{10}{R^2+L^2} (L cos⁡t – R sin⁡t + Le^{\frac{-Rt}{L}})\)
Answer» D. \(\frac{10}{R^2+L^2} (L cos⁡t – R sin⁡t + Le^{\frac{-Rt}{L}})\)

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?

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