Question

Determine $v_{o}$ in the circuit of Fig. 10.52

   Determine $v_{o}$ in the circuit of Fig. 10.52

Fundamentals of Electric Circuits

Fundamentals of Electric Circuits

Charles K.… 3rd Edition

Chapter 10, Problem 3

Instant Answer

Solved by Expert Varsha Aggarwal

02/07/2022

Step 1

The impedance of the inductor is given by $j\omega L$ and the impedance of the capacitor is given by $1/j\omega C$. Here, $\omega = 240$ rad/s, $L = 2$ mH, and $C = 12$ μF. So, we have: \[ Z_L = j\omega L = j240 \times 2 \times 10^{-3} = j0.48 \, Show more…

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Determine $v_{o}$ in the circuit of Fig. 10.52

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Key Concepts

Ohm's Law

Ohm's Law is a fundamental principle in electrical circuits that relates the voltage (V), current (I), and resistance (R) through the equation V = I × R. This law is essential for analyzing circuits because it allows for the calculation of the voltage drop across individual resistors when the current flowing through them is known, or vice versa.

Kirchhoff's Voltage Law (KVL)

Kirchhoff's Voltage Law states that the sum of the electrical potential differences (voltages) around any closed network is zero. This principle is used to write loop equations in circuit analysis, ensuring that all gains and drops in potential are accounted for, which is crucial when determining unknown voltages in a circuit.

Kirchhoff's Current Law (KCL)

Kirchhoff's Current Law states that the total current entering a junction must equal the total current leaving that junction. This conservation principle for electric charge is vital for analyzing current distributions in a circuit, particularly when using node analysis methods to determine unknown voltages or currents.

Node Voltage Analysis

Node Voltage Analysis is a systematic method used in circuit analysis that involves selecting nodes in a circuit and applying Kirchhoff's Current Law to each node. By expressing the differences in electrical potentials and incorporating Ohm's Law, a system of equations is formed that can be solved to find unknown node voltages and, subsequently, other quantities like branch currents and output voltage.

Mesh Analysis

Mesh Analysis is another systematic technique in circuit theory which involves writing equations around closed loops (meshes) in the circuit using Kirchhoff's Voltage Law. This method simplifies the analysis by reducing the number of equations needed for planar circuits, making it useful when finding unknown currents in various circuit loops.

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