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Answer :
Final answer:
The magnitude of the frequency generator changes because the impedance of circuit elements, represented by the ratio Z = V/I, varies with the frequency of the source. Circuit components like inductors and capacitors have frequency-dependent responses, altering the current in the circuit. Also, according to Faraday's Law, changes in the rotation frequency of a generator loop affect the induced voltage and current.
Explanation:
The magnitude of the frequency generator changes as we vary the frequency because in an alternating current (AC) circuit, the properties of the circuit elements can vary with frequency. For instance, the impedance (Z = V/I), where V is voltage and I is current, depends on the frequency of the source. This is because circuit elements like inductors and capacitors react differently at different frequencies due to their reactive components, which are frequency dependent.
When dealing with a circuit's response to an AC signal, assuming a complex exponential form for sources allows all voltages and currents to also be complex exponentials with the same frequency as the source. This simplifies analysis as the ratio of voltage to current (impedance) for circuit elements remains constant over time, though it changes with the source frequency. When you vary the frequency of the source, such as an AC generator, the circuit's impedance changes, which then affects the current, assuming the voltage amplitude stays constant. At resonant frequency, or in a purely resistive circuit where Z = R, the impedance is purely resistive, and voltage and current are in phase (cos = 1).
The induced potential in a generator, according to Faraday's Law, is dependent on the rate of change of magnetic flux, which itself is influenced by the frequency of rotation of the generator's loop in a magnetic field. Therefore, as the frequency of rotation changes, so does the induced voltage and consequent current if resistance is fixed.
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