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?

(a) Inductor and capacitor
(b) Resistor and inductor
(c) Resistor and capacitor
(d) Resistor, inductor, and capacitor

Choose the correct option.

1. (b, c)
2. (c, d)
3. (b, d)
4. (a, d)

(4) Hint: The current in the circuit depends on the impedance.
Step 1: The reactance of an inductor of inductance L is, XL=2πfL
where v is the frequency of the AC circuit.
Xc= Reactance of the capacitive circuit
=12πfC
Step 2: On increasing frequency v, clearly XL increases and XC decreases.
For a L-C-R circuit,
Z = impedance of the circuit
=R2+(XL-XC)2
=R2+2πfL-12πfC2
Step 3: As frequency (f) increases, Z decreases and at certain value of frequency known as resonant frequency (f0), impedance Z is minimum that is Zmin=R, the current varies inversely with impedance and at Zmin current is maximum.