Given the network shown in Figure P6.21, determine the value of the capacitor C that will cause

step 1 Hello friends here we have to find equivalent capistines of the given circuit. So we have to use

Given the network shown in Figure P6.21, determine the value...

Key Concepts

Resonance (Reactive Cancellation)

Resonance in an electrical network occurs when the reactive components (inductive and capacitive) cancel each other out, resulting in a net impedance that is purely resistive. By selecting the value of a capacitor to counterbalance the inherent inductive reactance in the circuit, the overall reflected impedance can be tuned to have no imaginary part. This principle is widely used to maximize power transfer and minimize phase differences.

Capacitive Reactance

Capacitive reactance is the opposition offered by a capacitor to AC, which decreases with increasing frequency. In networks where both inductive and capacitive elements are present, choosing the correct value of capacitor can be instrumental in neutralizing unwanted reactance. By offsetting the circuit’s inductive properties, capacitive reactance plays a pivotal role in achieving a purely resistive impedance at a target frequency.

Reflected Impedance

Reflected impedance is the effective impedance seen at the primary side of a transformer due to a load connected to the secondary side. This impedance is transformed by the square of the turns ratio of the transformer, meaning that any impedance (resistive or reactive) on the secondary appears at the primary scaled accordingly. Recognizing how the load is reflected is key to analyzing the overall circuit behavior.

Transformer Turns Ratio

The turns ratio of a transformer determines how voltages and impedances are scaled between the primary and secondary windings. Specifically, the load impedance on the secondary side is multiplied by the square of the transformer’s turns ratio to yield the reflected impedance. This concept is critical when designing circuits to achieve impedance matching or to cancel unwanted reactive effects.

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