Important MCQ of RC Circuit with Explanation – 2022 | RC Circuit MCQ

Ques.1. A positive angle of 60° is equivalent to a negative angle of

−300°

−330°

−240°

−360°

Answer.1. −300°

Explanation:-

We subtract 360 from the angle to get its corresponding negative angle.

60° = 60 – 360 = − 300°

Ques.2. When the frequency of the source voltage decreases, the impedance of an RC circuit

Remain Same

Decrease

Increase

None of the above

Answer.3. Increase

Explanation:-

As we know, capacitive reactance varies inversely with frequency.

The impedance of the RC circuit is given as

$Z = \sqrt {{R^2} + {X^2}_C}$

When X_{C} increases, the entire term under the square root sign increases, and thus the magnitude of the total impedance also increases; and when X_{C} decreases, the magnitude of the total impedance also decreases. Therefore, in a series RC circuit, Z is inversely dependent on frequency.

As the frequency is increased, X_{C} decreases; so less voltage is dropped across the capacitor. Also, Z decreases as X_{C} decreases, causing the current to increase. An increase in the current causes more voltage across R.

As the frequency is decreased, increases, X_{C} so more voltage is dropped across the capacitor. Also, Z increases as X_{C} increases, causing the current to decrease. A decrease in the current causes less voltage across R.

As the frequency increases, the voltage across Z remains constant because the source voltage is constant. Also, the voltage across C decreases. The increasing current indicates that Z is decreasing. It does so because of the inverse relationship stated in Ohm’s law i.e Z = V_{s}/I. The increasing current also indicates that X_{C} is decreasing (X_{C} = V_{c}/I). The decrease in V_{c }corresponds to the decrease in X_{C}.

Since X_{C} is the factor that introduces the phase angle in a series RC circuit, a change in X_{C} produces a change in the phase angle. As the frequency is increased, becomes smaller, and thus the phase angle decreases. As the frequency is decreased, X_{C} becomes larger, and thus the phase angle increases.

Ques.3. The complex number 6 + j6 is equivalent to

8.48 ∠90°

Answer.2. 8.48 ∠45°

Explanation:-

The magnitude of the phasor represented by 6 + j6 is

$\begin{array}{l} C = \sqrt {{A^2} + {B^2}} \\ \\ C = \sqrt {{8^2} + {6^2}} \end{array}$

C = 8.48

Since the phasor is in the first quadrant, therefore, the angle is

θ = tan^{−1}(±B/A)

θ = tan^{−1}(6/6) = 45°

θ is the angle relative to the positive real axis. The polar form of 8 + j6 is

C∠θ = 8.48∠45°

Ques.4. In an RC circuit, the impedance is determined by both the ______ and the ________combined.

Ques.5. The conversion of 10∠30° from polar quantities to rectangular form is

8.66 + j5

8.66 − j5

4.66 + j5

4.66 − j5

Answer.1. 8.66 + j5

Explanation:-

The real part of the phasor represented by 10∠30° is

A = C.cosφ

= 10 cos 30° = 10(0.866) = 8.66

The imaginary part j of the phasor is

jB = jC sinφ

= j10 sin 30° = j10(0.5) = j5

The rectangular form of 10∠30° is

A + jB = 8.66 + j5

Ques.6. The RC capacitor circuit the capacitor voltage always leads the current by ______

90°

45°

0° to 90°

0°

Answer.3. 0° to 90°

Explanation:-

When a sinusoidal voltage is applied to a series RC circuit, each resulting voltage drop and the current in the circuit are also sinusoidal and have the same frequency as the applied voltage. The capacitance causes a phase shift between the voltage and current that depends on the relative values of the resistance and the capacitive reactance.

As shown in Figure, the resistor voltage V_{R} the capacitor voltage V_{C} and the current (I) are all sine waves with the frequency of the source. Phase shifts are introduced because of the capacitance. The resistor voltage and current lead to the source voltage, and the capacitor voltage lags the source voltage. The phase angle between the current and the capacitor voltage is always 90°.

The amplitudes and the phase relationships of the voltages and current depend on the resistance and capacitive reactance values. When a circuit is purely resistive, the phase angle between the applied (source) voltage and the total current is zero.

When a circuit is purely capacitive, the phase angle between the applied voltage and the total current is 90° with the current leading the voltage. When there is a combination of both resistance and capacitive reactance in a circuit, the phase angle between the applied voltage and the total current is somewhere between 0° and 90° depending on the relative values of the resistance and the capacitive reactance.

Ques.7. Conversion of 8 + j6 complex numbers from rectangular form to polar form is

20∠36.9°

10∠63.9°

20∠63.9°

10∠36.9°

Answer.4. 10∠36.9°

Explanation:-

The magnitude of the phasor represented by 8 + j6 is

$\begin{array}{l} C = \sqrt {{A^2} + {B^2}} \\ \\ C = \sqrt {{8^2} + {6^2}} \end{array}$

C = 10

Since the phasor is in the first quadrant, therefore, the angle is

θ = tan^{−1}(±B/A)

θ = tan^{−1}(6/8) = 36.9°

θ is the angle relative to the positive real axis. The polar form of 8 + j6 is

C∠θ = 10∠36.9°

Ques.8. The complex plane, the number 24 – j8 is located in

1st Quadrant

2nd Quadrant

3rd Quadrant

4th Quadrant

Answer.4. 4th Quadrant

Explanation:-

A phasor can be visualized as forming a right triangle in the complex plane, as indicated in Figure, for each quadrant location. The horizontal side of the triangle is the real value, A, and the vertical side is the j value, B. The hypotenuse of the triangle is the length of the phasor, C, representing the magnitude, and can be expressed, using the Pythagorean theorem, as

$C = \sqrt {{A^2} + {B^2}} $

So from the above figure, it is clear that the number 24 – j8 is located in the fourth quadrant.

Ques.9. The total current in an RC circuit ______ the source voltage.

Lag

Lead

Maybe lead or lag

None of the above

Answer.4. Lead

Explanation:-

In a series RC circuit, the current is the same through both the resistor and the capacitor. Thus, the resistor voltage is in phase with the current, and the capacitor voltage lags the current by 90°. Therefore, there is a phase difference of 90° between the resistor voltage, V_{R,} and the capacitor voltage V_{C}, as shown in the waveform diagram.

Ques.10. The complex number 200∠-45° is equivalent to

141 + j141

1.41 + j1.41

1.41 − j1.41

141 − j141

Answer.4. 141 − j141

Explanation:-

The real part of the phasor represented by 10∠30° is