A coil has resistance of 1 Ω and an inductance of 1 H. When it is connected to 6 V DC voltage source, calculate initial and final values of current using Laplace transform method.a.0 A, 6 Ab. 1 A, 3 Ac.1 A, 6 Ad.0 A, 3 AClear my choice
Question
A coil has resistance of 1 Ω and an inductance of 1 H. When it is connected to 6 V DC voltage source, calculate initial and final values of current using Laplace transform method.a.0 A, 6 Ab. 1 A, 3 Ac.1 A, 6 Ad.0 A, 3 AClear my choice
Solution
The Laplace transform method is a mathematical technique used to solve differential equations. In this case, we can use it to solve for the current in an RL circuit.
Step 1: Formulate the differential equation The differential equation for an RL circuit is V = L(di/dt) + Ri, where V is the voltage, L is the inductance, R is the resistance, and i is the current. Substituting the given values, we get 6 = 1*(di/dt) + 1*i.
Step 2: Take the Laplace transform Taking the Laplace transform of both sides of the equation, we get 6/s = (1/s)*(I(s) - i(0)) + I(s), where I(s) is the Laplace transform of the current and i(0) is the initial current.
Step 3: Solve for I(s) Rearranging the equation, we get
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