TOP RLC Circuit Questions and Answers with explanation – 2022

MCQ / March 15, 2022

Ques.31. The impedance in parallel RLC circuit is given as

(1) $\frac{1}{Z} = \frac{1}{{R\angle 0^\circ }} + \frac{1}{{{X_L}\angle 0^\circ }} + \frac{1}{{{X_C}\angle 0^\circ }}$

 

(2) $\frac{1}{Z} = \frac{1}{{R\angle 0^\circ }} + \frac{1}{{{X_L}\angle 90^\circ }} + \frac{1}{{{X_C}\angle 90^\circ }}$

 

(3) $\frac{1}{Z} = \frac{1}{{R\angle 0^\circ }} + \frac{1}{{{X_L}\angle 90^\circ }} + \frac{1}{{{X_C}\angle – 90^\circ }}$

 

(4) $\frac{1}{Z} = \frac{1}{{R\angle 0^\circ }} – \frac{1}{{{X_L}\angle 90^\circ }} – \frac{1}{{{X_C}\angle – 90^\circ }}$

 

Answer.3. $\frac{1}{Z} = \frac{1}{{R\angle 0^\circ }} + \frac{1}{{{X_L}\angle 90^\circ }} + \frac{1}{{{X_C}\angle – 90^\circ }}$

Explanation:-

The figure shows a parallel RLC circuit. The total impedance can be calculated using the reciprocal of the sum-of-reciprocals method, just as was done for circuits with resistors in parallel.

Parallel RLC Circuit

The impedance of parallel RLC circuit is given as

$\frac{1}{Z} = \frac{1}{{R\angle 0^\circ }} + \frac{1}{{{X_L}\angle 90^\circ }} + \frac{1}{{{X_C}\angle – 90^\circ }}$

 

Ques.32. For parallel RLC circuits, the phasor expression for Conductance (G) is

  1. G∠90°
  2. G∠180°
  3. G∠−90°
  4. G∠0°

Answer.4. G∠0°

Explanation:-

The conductance, G, is the reciprocal of resistance. The phasor expression for conductance is expressed as

G = 1/R∠0° = G∠0°

 

Ques.33. For parallel RLC circuits, the phasor expression for Capacitive susceptance (BC) is

  1. jBC
  2. −jBC
  3. 2jBL
  4. None of the above

Answer.1. jBC

Explanation:-

Capacitive susceptance (BC) is the reciprocal of capacitive reactance. The phasor expression for capacitive susceptance is

BC = 1/XC∠−90°

BC = ∠90° = jBC

 

Ques.35. For parallel RLC circuits, the phasor expression for inductive susceptance (BL) is

  1. jBL
  2. −jBL
  3. 2jBL
  4. None of the above

Answer.1. jBL

Explanation:-

For parallel RL circuits, the phasor expression for inductive susceptance (BL) is

BL = 1/XL∠90°

BL∠−90° = −jBL

 

Ques.34. For parallel RLC circuits, the phasor expression for Admittance (Y) is

  1. Y∠θ
  2. Y∠−θ
  3. Y∠2θ
  4. Y∠±θ

Answer.4. Y∠±θ

Explanation:-

Admittance (Y) is the reciprocal of impedance. The phasor expression for admittance is

Y = 1/Z∠ ±θ

Y = ∠ ±θ

 

Ques.35. In a parallel RLC Resonant circuit, the current in the capacitive branch and the current in the inductive branch are always ____ with each other.

  1. 90° out of phase
  2. 180° out of phase
  3. 180° in  phase
  4. 90° in phase

Answer.2. 180° out of phase

Explanation:-

Parallel Resonant Circuits

A parallel resonant circuit is formed when the Inductor and capacitor are connected in parallel with the applied voltage. In general, resonance in a parallel tuned circuit can also be defined as the point at which the inductive and capacitive reactances are equal.

RLC.img .7

If we assume lossless components in the circuit (no resistance), then the current in Parallel resonant circuit the inductor equals the current in the capacitor: Although the currents are equal, they are 180° out of phase, as the phasor diagram in Fig The current in the inductor lags the applied voltage by 90°, and the current in the capacitor leads the applied voltage by 90°, for a total of 180°.

 

Ques.36. Ideally, the parallel resonance occurs when the

  1. XL > XC
  2. XL < XC
  3. XL > 2XC
  4. XL = XC

Answer.4. XL = XC

Explanation:-

The circuit, with resistance R, inductance L, and capacitance, C in parallel is connected to a single-phase variable frequency (f) supply is called a parallel resonance circuit. The condition for resonance occurs when the susceptance part is zero.

The total admittance of the circuit is

Y = YR + YL + YC

= 1/R + 1/jXL  + 1/(−jXC)

= 1/R + j(1/XL − 1/XC)

At resonance condition, the “j” component of admittance is equal to zero.

1/XL − 1/XC = 0

XL = XC

Ideally, parallel resonance occurs when XL = XC. When XL = XC the two branch currents, and are equal in magnitude, and they are always 180° out of phase with each other.

 

Ques.37. Ideally the parallel Resonance circuit is one that contain only _____ and _______

  1. Inductance, capacitance
  2. Inductance, Resistance
  3. Resistance, capacitance
  4. None of the above

Answer.1. Inductance, capacitance

Explanation:-

The ideal parallel resonant circuit is one that contains only inductance and capacitance. Resistance and its effects are not considered in an ideal parallel resonant circuit, One condition for parallel resonance is the application of that frequency which will cause the inductive reactance to equal the capacitive reactance.

 

Ques.38. The total current in the parallel resonance circuit is given by the expression

(1) ${I_t} = \sqrt {I_R^2 + {{({I_C} – {I_L})}^2}} \angle {\tan ^{ – 1}}\left( {\frac{{{I_C}_L}}{{{I_R}}}} \right)$

 

(2) ${I_t} = \sqrt {I_R^2 + {{({I_C} + {I_L})}^2}} \angle {\tan ^{ – 1}}\left( {\frac{{{I_C}_L}}{{{I_R}}}} \right)$

 

(3) ${I_t} = \sqrt {I_R^2 – {{({I_C} + {I_L})}^2}} \angle {\tan ^{ – 1}}\left( {\frac{{{I_C}_L}}{{{I_R}}}} \right)$

 

(4) ${I_t} = \sqrt {I_R^2 – {{({I_C} – {I_L})}^2}} \angle {\tan ^{ – 1}}\left( {\frac{{{I_C}_L}}{{{I_R}}}} \right)$

 

Answer.1. ${I_t} = \sqrt {I_R^2 + {{({I_C} – {I_L})}^2}} \angle {\tan ^{ – 1}}\left( {\frac{{{I_C}_L}}{{{I_R}}}} \right)$

Explanation:-

In a parallel RLC circuit, the current in the capacitive branch and the current in the inductive branch are always 180° out of phase with each other (neglecting any coil resistance). Because IC and IL add algebraically, the total current is actually the difference in their magnitudes. Thus, the total current into the parallel branches of L and C is always less than the largest individual branch current.

The current in the resistive branch is always 90° out of phase with both reactive currents.

The total current can be expressed as

${I_t} = \sqrt {I_R^2 + {{({I_C} – {I_L})}^2}} \angle {\tan ^{ – 1}}\left( {\frac{{{I_C}_L}}{{{I_R}}}} \right)$

where ICL is (IC − IL) the total current into the L and C branches.

 

Ques.39. A parallel resonance circuit is also called as an

  1. Acceptor circuit
  2. Deflector circuit
  3. Rejector circuit
  4. Donor circuit

Answer.3. Rejector circuit

Explanation:-

A parallel resonant circuit, therefore, admits a very minimum current at the resonant frequency. Therefore it can be employed as a “wave-trap” to block as completely as possible any unwanted frequency by tuning the circuit to be resonant at that frequency, Hence the name ‘rejector resonance’ to the parallel resonance.

 

Ques.40. The current in the perfect parallel resonance circuit is at _______ value.

  1. Maximum
  2. Zero
  3. Minimum
  4. Infinite

Answer.2. Zero 

Explanation:-

At a particular frequency (known as the parallel resonant frequency) the reactance of the capacitor, XC, will be equal in magnitude (but of opposite sign) to that of the inductor, XL. When XL = XC the two branch currents, and are equal in magnitude, and, of course, they are always 180° out of phase with each other. Thus, the two currents cancel and the total current is zero in the case of a perfect parallel resonant circuit).

When XL = XC the two branch currents, and are equal in magnitude, and, of course, they are always 180° out of phase with each other. Thus, the two currents cancel and the total current is zero.

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