Math Problem Statement
an RL circuit has an emf given (in volts) by 3sin2t, a resistance of 10 ohms, an inductance of 0.5 henry, and an initial current of 6 amperes. fine the current in the circuit at any time t. give correct solution and answer
Solution
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Math Problem Analysis
Mathematical Concepts
Differential Equations
RL Circuit
Kirchhoff's Voltage Law
Transient and Steady-State Behavior
Formulas
Kirchhoff's Voltage Law: L(dI/dt) + RI = V(t)
General Solution: I(t) = I_h(t) + I_p(t)
Homogeneous Solution: I_h(t) = C_2 * e^(-20t)
Particular Solution: I_p(t) = A * cos(2t) + B * sin(2t)
Theorems
Separation of Variables
Method of Undetermined Coefficients
Suitable Grade Level
Undergraduate Electrical Engineering or Physics
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