When an electrical circuit has inductance L, resistance R, capacitance C, and applied voltage v(t)placed in the charge q(t) in the capacitor satisfies the differential equation1Lq"(t) + Rq'(t) + —q(t):q(t) = v(t).An electrical engineer is experimenting to see how such circuits responds to a brief applied voltage2 sin(t), 0 T"(a) Express v(t) in terms of the unit step function, and hence evaluate L {v(t)}.mas(t) =(b) Use the trigonometric identity 2 sin(a) sin(ba) = cos(2a - b) cos(b)theorem [LT17] to calculate2C• ¹{²}\(s² + 1)²-College Pliageand the convolution(c) Using parts (a) and (b), determine an expression for q(t) for a circuit with applied voltagev(t), an inductance of 1 henry, a capacitance of 1 farad, no resistance, and no charge in thecapacitor nor current in the circuit (that is, q(0) = 0 and q'(0) = 0). Write your final answeras a piecewise function covering the cases where 0 < t < and t≥ π.Note: State each Laplace transform property as you use it. Refer to each property using its rownumber in the Table of Laplace Transforms provided. For example, "C{1} = by [LT1]."

Given Equation: Lq"(t)+Rq'(t)+1cq(t)=V(t)Ld2qdt2+Rdqdt+1cq=V(t)V(t)=2 sin(t)0<t<π0t≥π

When an electrical circuit has inductance L, resistance R, capacitance C, and applied voltage v(t) placed in series, the charge q(t) in the capacitor satisfies the differential equation 1 Lq"(t) + Rq' (t) + —q(t) = v(t). An electrical engineer is experimenting to see how such circuits responds v(t) = 0, t> π C- (a) Express v(t) in terms of the unit step function, and hence evaluate L {v(t)}. (b) Use the trigonometric identity 2 sin(a) sin(ba) = cos(2a - b) - theorem [LT17] to calculate - 2 { (8² + 1)²) to a brief oplied voltage =}. and the convolution (c) Using parts (a) and (b), determine an expression for q(t) for a circuit with applied voltage v(t), an inductance of 1 henry, a capacitance of 1 farad, no resistance, and no charge in the capacitor nor current in the circuit (that is, q(0) = 0 and q'(0) = 0). Write your final answer as a piecewise function covering the cases where 0 < t < and t > T. Note: State each Laplace transform property as you use it. Refer to each property using its row number in the Table of Laplace Transforms provided. For example, "C{1}=by [LT1]."

When an electrical circuit has inductance L, resistance R, capacitance C, and applied voltage v(t) placed in series, the charge q(t) in the capacitor satisfies the differential equation 1 Lq"(t) + Rq' (t) + —q(t) = v(t). An electrical engineer is experimenting to see how such circuits responds v(t) = 0, t> π C- (a) Express v(t) in terms of the unit step function, and hence evaluate L {v(t)}. (b) Use the trigonometric identity 2 sin(a) sin(ba) = cos(2a - b) - theorem [LT17] to calculate - 2 { (8² + 1)²) to a brief oplied voltage =}. and the convolution (c) Using parts (a) and (b), determine an expression for q(t) for a circuit with applied voltage v(t), an inductance of 1 henry, a capacitance of 1 farad, no resistance, and no charge in the capacitor nor current in the circuit (that is, q(0) = 0 and q'(0) = 0). Write your final answer as a piecewise function covering the cases where 0 < t < and t > T. Note: State each Laplace transform property as you use it. Refer to each property using its row number in the Table of Laplace Transforms provided. For example, "C{1}=by [LT1]."

Delmar's Standard Textbook Of Electricity

7th Edition

ISBN:9781337900348

Author:Stephen L. Herman

Publisher:Stephen L. Herman

Chapter20: Capacitance In Ac Circuits

Section: Chapter Questions

Problem 5PP: Three capacitors having capacitance values of 20F,40F, and 50F are connected in parallel to a 60 -...

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