Ncert Exercises & Solutions

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 options:
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,

X_{L} = 2 πfL

where v is the frequency of the AC circuit.

X_{c}

= Reactance of the capacitive circuit

= \frac{1}{2 πfC}

Step 2: On increasing frequency v, clearly

X_{L}

increases and

X_{C}

decreases.

For

a L - C - R

circuit,

Z = impedance of the circuit

= \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}

= \sqrt{R^{2} + {(2 πfL - \frac{1}{2 πfC})}^{2}}

Step 3: As frequency (f) increases, Z decreases and at certain value of frequency known as resonant frequency

(f_{0})

, impedance Z is minimum that is

Z_{\min} = R

, the current varies inversely with impedance and at

Z_{\min}

current is maximum.

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