Electric Circuit

Step 1: Recall the definition of the Quality Factor (Q). The quality factor of a resonant circuit is a measure of its selectivity. It is defined as the ratio of the resonant frequency ( ) to the bandwidth (BW).
Step 2: Identify the given values. Resonant frequency, . Quality factor, .
Step 3: Calculate the bandwidth. Rearrange the formula to solve for BW: Substitute the given values: Convert the result to kilohertz:

Step 1: Define Nodal Analysis. Nodal analysis is a technique used to determine the voltage at each node (a point where two or more circuit elements connect) relative to a reference node.
Step 2: Identify the foundational laws used. The primary principle of nodal analysis is Kirchhoff's Current Law (KCL). KCL states that the algebraic sum of currents entering a node must be zero. An equation based on KCL is written for each unknown node voltage.
Step 3: Identify the law used to express the currents. The currents flowing between nodes are typically unknown. To express these currents in terms of the node voltages (which are the variables we want to solve for), we use Ohm's Law. For a resistor R between nodes A and B with voltages and , the current is .
Step 4: Conclude the basis of the method. Since the nodal equations are formulated using KCL, and the terms within those equations are derived using Ohm's Law, the nodal method is based on KCL and Ohm's law. Kirchhoff's Voltage Law (KVL) is the foundation for the alternative method, Mesh Analysis.

Step 1: Interpret the complex circuit diagram. The diagram shows a Wheatstone bridge configuration. The symbols for sources inside the diagram are confusing. A common simplification for such problems is to assume a single excitation source across the main terminals of the bridge and that the internal symbols are for reference. Let's assume the bridge is excited by a 1V source connected between the top and bottom nodes. The inductor with impedance is in the top-right arm of the bridge.
Step 2: Analyze the bridge under this assumption. Let the top node be A and the bottom node be B, so . The bridge has two parallel branches connected across A and B. Branch 1 (left side): A resistor in series with a capacitor. Total impedance . Branch 2 (right side): A resistor in series with the inductor. Total impedance . The question asks for the current through the inductor, which is the current flowing through Branch 2.
Step 3: Calculate the current through the inductor's branch. Using Ohm's law, the current flowing through the right branch is the voltage across the branch divided by the impedance of the branch. Substituting the values: This result matches one of the options. Alternative Interpretation (Bridge Balance): Let's check if the bridge is balanced. The arms are . The balance condition is . . . Since , the bridge is balanced. This means the potential of the two middle nodes are equal. However, the inductor is not in the central arm, it is one of the main arms of the bridge, so its current is not zero. The first interpretation leading to an answer is the most likely intended one.