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Question
As the frequency of an ac circuit increases, the current first increases and then decreases. What combination of circuit elements is most likely to comprise the circuit?
- Inductor and capacitor.
- Resistor and inductor.
- Resistor and capacitor.
- Resistor, inductor and capacitor.
Options
a and b
b and c
c and d
a and d
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Solution
a and d
Explanation:
Compare the given circuit by predicting the variation in their reactances with frequency. So, that then we can decide the elements.
Reactance of an inductor of inductance L is XL = 2πvL, where v is the frequency of the AC circuit.
XC = Reactance of the capacitive circuit = `1/(2pi fC)`
With an increase in frequency `(f)` of an AC circuit, R remains constant, inductive reactance (XL) increases and capacitive reactance (XC) decreases.
For an L-C-R circuit,
Z = Impedance of the circuit
= `sqrt(R^2 + (X_L - X_C)^2)`
= `sqrt(R^2 + (2pivL - 1/(2pivC)^2)`
As frequency (v) increases, Z decreases and at certain value of the frequency known as resonant frequency (v0), impedance Z is minimum that is Zmin = R current varies inversely with impedance and at Zmin current is maximum.
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