Sate the definition of a branch circuit.

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Chapter 3, Problem 25R

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Sate the definition of a branch circuit.

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Q2)a) consider the Circuit in figure 2 with initial conditions of Vc (o) = 5V, I₁ (o) = 1A, (i) redraw the circuit in the frequency domain using laplace Wansforms. (ii) using this circuit derive an equation for the Voltage across the inductor in the time domain.. 3.12 ww =V/3F ZH (figure 2) d) Solve the following second order differential equation using laplace transforms. d12 + 5 dx 3x=71 dt - with initial conditions x² (0) = 2, α(0) = 1

b) Another periodic waveform is defined by T c) g(t)= T with g(t+mT) = g(t) and m is an integer. (i) Sketch g(t) over two full cycles in the time domain, labelling the axes. (ii) Derive the formulae for the complex Fourier coefficients c₁ for g(t). For a periodic waveform h(t), if its complex Fourier coefficients are T T when n is odd T 2n²² T 4nn when n is even and not zero 4nn please derive the first five non-zero terms of the real Fourier series for h(t).

Q3)α) f(t) = (-+- 1 Isto f(t+mT) = f(t). L+- I Ost ST integer (i) sketch f(t) 2 full cycles time domain. (labelling the axis). (ii) Derive the formula for the real fourier Coefficients (i) Real Fourier series f(t), first 5 non-terms. an bn for f(t).