Explore topic-wise MCQs in Ordinary Differential Equations.

This section includes 3 Mcqs, each offering curated multiple-choice questions to sharpen your Ordinary Differential Equations knowledge and support exam preparation. Choose a topic below to get started.

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}}) )
Discussion
2.

A voltage Ee-at is applied at t=0 to a circuit containing inductance L and resistance R. Determine the current at any time t.

A. ( frac{Ee^{-at}}{L-Ra} left(e^{ frac{-Rt}{L}} right) )
B. ( frac{E}{R-La} left(e^{-at}-e^{ frac{-Rt}{L}} right) )
C. ( frac{E}{La} left(e^{-at}+e^{ frac{Rt}{L}} right) )
D. ( frac{Ee^{-at}}{R} left(1-e^{ frac{-Rt}{L}} right) )
Answer» C. ( frac{E}{La} left(e^{-at}+e^{ frac{Rt}{L}} right) )
Discussion
3.

A constant electromotive force E volts is applied to a circuit containing a constant resistance R ohm in series with a constant inductance L henries. If the initial current is zero. What is the current in the circuit at any time t?

A. ( frac{E}{R} left(1-e^{ frac{-Rt}{L}} right) )
B. ( frac{E}{R} left(e^{ frac{Rt}{L}} right) )
C. ( frac{E}{L} (1-e^{RLt}) )
D. ( frac{E}{L} (e^{-RLt}) )
Answer» B. ( frac{E}{R} left(e^{ frac{Rt}{L}} right) )
Discussion