LCR series circuit and resonance — NEET & JEE Questions

Question 1 · difficulty L1 · recall

Series resonance in an RLC circuit occurs when

• A. XL=XC
• B. XL=R
• C. XC=R
• D. XL+XC=0 only if both are zero

Question 2 · difficulty L1 · understanding

At resonance, the impedance of a series RLC circuit is

• A. XL+XC
• B. R
• C. zero even when R is nonzero
• D. sqrt(R²+4XL²)

Question 3 · difficulty L2 · understanding

The resonant angular frequency of an ideal series RLC circuit is

• A. sqrt(LC)
• B. R/L
• C. 1/sqrt(LC)
• D. 1/(RC)

Question 4 · difficulty L2 · application

At series resonance, current amplitude for a given applied voltage is

• A. minimum
• B. zero
• C. independent of resistance
• D. maximum

Question 5 · difficulty L2 · understanding

A resonance circuit having inductance and resistance 2 $$\times$$ 10 $$-$$4 H and 6.28$$\Omega$$ respectively oscillates at 10 MHz frequency. The value of quality factor of this resonator is ___________. [$$\pi$$ = 3.14]

Question 6 · difficulty L3 · application

At resonance, the phase difference between source voltage and current in a series RLC circuit is

• A. zero
• B. 90° with current leading
• C. 90° with current lagging
• D. 180°

Question 7 · difficulty L3 · application

If L is increased while C is fixed, the resonant frequency

• A. increases
• B. decreases
• C. remains fixed
• D. becomes zero for any increase

Question 8 · difficulty L3 · application

A series LCR circuit has L = 10 mH and C = 1 $\mu$F. Its resonant angular frequency is

• A. 10$^{-4}$ rad s$^{-1}$
• B. 10$^8$ rad s$^{-1}$
• C. 10$^4$ rad s$^{-1}$
• D. 10$^2$ rad s$^{-1}$

Question 9 · difficulty L3 · application

A series LCR circuit with R = 10 $\Omega$ is driven at its resonant frequency by a 100 V (rms) source; at resonance $X_L$ = $X_C$ = 50 $\Omega$. The rms current and the rms voltage across the inductor are

• A. 2 A and 100 V
• B. 10 A and 100 V
• C. 1 A and 50 V
• D. 10 A and 500 V

Question 10 · difficulty L4 · analysis

A series RLC circuit has L=1 H and C=1 μF. Its resonant angular frequency is

• A. 100 rad s^-1
• B. 10^6 rad s^-1
• C. 1000 rad s^-1
• D. 1 rad s^-1