3 Find $V_{out}$ assuming initial zero initial conditions 4 (H) $\frac{1}{3}$ F 5$\Omega$ 1H $V_o(t)$
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Step 1: The circuit is a series RLC circuit with a resistor of 5 ohms, an inductor of 1 henry, and a capacitor of 1/3 farad. Show more…
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Adi S.
Calculate the voltage labeled vx in Fig. 7.51, assuming the circuit has been running for a very long time, if (a) a 10 Ω resistor is connected between terminals x and y; (b) a 1 H inductor is connected between terminals x and y; (c) a 1 F capacitor is connected between terminals x and y; (d) a 4 H inductor in parallel with a 1 Ω resistor is connected between terminals x and y. (a) -5 + V / 27 + V / 30 + (V - 1) / 20 = 0 Solving, V = 41.95 V. By voltage division, Vx = (12/27)(41.95) = 18.64 V. (b) -5 + V / 27 + V / 20 + (V - 1) / 20 = 0 Solving, V = 36.85 V. By voltage division, Vx = (12/27)(36.85) = 16.38 V. (c) -5 + V / 27 + (V - 1) / 20 = 0. V = 58.02 V. By voltage division, Vx = (12/27)(58.02) = 25.79 V. (d) Same as case (b): Vx = 16.38 V.
Sri K.
In Exercises $35-38,$ consider a series circuit (Figure 4) consisting of a resistor of $R$ ohms, an inductor of L. henries, and a variable voltage source of $V(t)$ volts (timet in seconds). The current through the circuit $I(t)$ (in amperes) satisfies the differential equation $$\frac{d I}{d t}+\frac{R}{L} I=\frac{1}{L} V(t)$$ Solve Eq. (9) with initial condition $I(0)=0,$ assuming that $R=100$ ohms $(\Omega), L=5$ henries $(\mathrm{H}),$ and $V(t)$ is constant with $V(t)=10$ volts $(\mathrm{V}) .$
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