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The correct choice is (b) 20 A

For explanation I would say: Given: efficiency (η) = 60%; Input power (PI) = 5 kW = 5000 W; VS = 150 V

Efficiency (η)=\(\frac {OUTPUT \, power (P_o)}{Input \, power (P_i)}=\frac {V_s I_s}{V_p I_p}\)

\(\frac {60}{100}=\frac {P_o}{5000}\)

Po=\(\frac {60 \TIMES 5000}{100}\)=3000 W

Thus,

Is=\(\frac {P_o}{V_s} = \frac {3000}{150}\)=20 A

Therefore, the current in the secondary coil is 20 A.

Right option is (B) 10 Ω

The EXPLANATION is: XC = XL.

C = \(\frac {1}{4π^2f^2L}\)

C = \(\frac {1 \times 7 \times 7}{(4 \times 22 \times 22 \times 70^2 \times 70 \times 10^{-3} )}\)

C = 7.37 × 10^-5 F.

Impedance (Z) = √(R^2 + (XL – XC)^2

Z = 10 Ω.

The correct option is (d) 1

Explanation: The IMPEDANCE for a series LCR circuit is given as:

Z=\(\sqrt {R^2+(X_L-X_C)^2}\)andcos⁡Φ=\(\frac {R}{Z}\)

At resonance, XL=XC ➔Z = R;

So, the total impedance of the circuit is only due to resistor. The phase ANGLE between voltage and current is zero. THEREFORE,

Φ=0 ➔ POWER factor (cosΦ)=1

Right answer is (c) SOFT iron

Explanation: Core of a transformer is used to transfer the flux produced by primary coils of transformer to secondary coils of a transformer. Therefore, the core of a transformer is made of soft iron because it has HIGH permeability so it provides complete linkage of MAGNETIC flux of the primary COIL to the secondary coil.

The correct ANSWER is (B) False

The best I can explain: No, this statement is false. The QUANTITY that remains unchanged in a transformer is the FREQUENCY of the input alternating current. Frequency of the alternating current at input = Frequency of the alternating current at output.

Correct choice is (b) Pav=\(\frac {V_o I_o}{2}\)cosΦ

The explanation is: AVERAGE power can be defined as the power AVERAGED over ONE full cycle of alternating current. It is ALSO known as true power. The EXPRESSION for average power is given by:

Pav=VrmsIrmscos⁡Φ=\(\frac {V_o I_o}{2}\)cosΦ

Correct choice is (c) Instantaneous power

The best I can explain: Instantaneous power is defined as the power in an AC circuit at any instant of TIME. It is EQUAL to the product of VALUES of alternating voltage and alternating current at that time. And, because instantaneous power varies in both magnitude and sign over a cycle, it seldom has any practical importance.

Correct CHOICE is (a) 636.6 Ω

To EXPLAIN I would SAY: Xc = \(\frac {1}{2πfC}\)

Xc = \(\frac {1}{(2 \TIMES 3.14 \times 50 \times 5 \times 10^{-6})}\)

Xc = 636.6 Ω.

Right answer is (a) True

Easy EXPLANATION: Yes, this is a true STATEMENT. The explanation is given as follows:

E = E0 sinωt.

Erms = \(\frac {E_0}{\sqrt {2}} = \frac {50}{\sqrt {2}}\)

Erms = 35.35 V.

IRMS = \(\frac {E_{rms}}{R} \, = \, \frac {35.5}{5} \)

Irms = 7.07 A.

Power dissipated = Ev × Iv = 35.35 × 7.07

Power dissipated = 249.92 W ≈ 250 W.

Right answer is (a) Transformers are used to convert low alternating voltage to a high alternating voltage

Best explanation: Transformers are used to convert low alternating voltage to a high alternating voltage and vice versa. Transformers are based on the phenomena of MUTUAL induction. A transformer consists of a soft iron coil with two coils WOUND around it which are not CONNECTED to one another. The other STATEMENTS are not VALID.

The correct OPTION is (a) LC Oscillations

To elaborate: This situation is caused due to LC Oscillations. These CIRCUITS consist capacitors and inductors, thus the energy keeps OSCILLATING in the circuit even after the electric connection is disconnected. The combination of a capacitor and an INDUCTOR constitutes an LC OSCILLATOR circuit.

Right CHOICE is (b) 0

To explain: A CIRCUIT which contains only INDUCTANCE is called a pure inductive circuit and a circuit containing only a pure capacitor is known as a pure CAPACITIVE circuit. In a pure inductive circuit or a pure capacitive circuit, the current is lagging or ahead by 90 degrees from the voltage. The power factor is the cosine of the angle between the voltage and the current. Therefore:

Φ = \(\frac {\pi}{2}\)➔ Power factor (cos⁡\(\frac {\pi}{2}\))=0

Correct option is (a) 3

The explanation: In an AC circuit, we can define three types of power, namely, Instantaneous power, Average power, and Apparent power. A circuit element produces or dissipates power ACCORDING to the EQUATION ➔ P = IV, where I is the current through the element and V is the voltage across it.

Correct option is (a) True

The explanation is: Yes, apparent power is also known as virtual power. Apparent power is defined as the product of virtual voltage (VRMS) and virtual current (Irms). It is the COMBINATION of REACTIVE power and true power and is measured in the unit of volt-amps (VA).

Pv=VrmsIrms=\(\frac {V_o I_o}{2}\)

Correct option is (B) False

Easiest explanation: GIVEN a current in SERIES LC, the voltage in inductor (L) leads current by 90° phase and voltage in capacitor (C) lags behind current by 90° phase. So voltage in inductor and capacitor DIFFER by a phase of 180°.

Correct choice is (d) Halved

The BEST I can explain: If the frequency is DOUBLED, the capacitive reactance is halved and CONSEQUENTLY, the CURRENT is doubled. This is because, when capacitive reactance, being a resistance, is lowered, the current can flow more EASILY through the circuit.

Right OPTION is (b) 2.07 A

For explanation I would say: PEAK current (I0) = \(\frac {E_0}{X_L}\)

I0 = \(\frac {650}{(2 \TIMES 3.14 \times 100 \times 0.5)}\)

I0 = 2.07 A

Therefore, the peak current is calculated as 2.07 A.

Right CHOICE is (b) Xc = \(\FRAC {1}{2πfC}\)

Explanation: For an ac CIRCUIT CONTAINING capacitor only,

Xc = \(\frac {1}{\omega_C}\)

Xc = \(\frac {1}{2πfC}\).

Right OPTION is (b) 1 mA

The BEST I can explain: I0 = \(\FRAC {E_0}{(\frac {1}{\omega C})}\)

I0 = ωCE0.

I0 = 10 × 10 × 10^-6 × 10

I0 = 10^-3A = 1 mA.

The correct CHOICE is (a) Maximum

The explanation: The current is ZERO when the COIL is vertical. In this position, flux through the coil is maximum. On the other hand, the current is maximum, when the coil is horizontal. So, when the current is zero, the flux through the coil is maximum.

Correct option is (c) 63 V

The best I can explain: e0 = nBAω.

e0 = 30 × 0.15 × 0.05 × 2π × (\(\FRAC {140}{\PI }\))

e0 = 63 V.

Correct ANSWER is (b) 2 A

The explanation is: Given: V2 = 10 V; V1 = 20 V; C = 5 μF; Inductance (I) = 0.5 mH

Initial charge on the capacitor (q1) = C × V1 = 5 × 10^-6 × 20 ……………….1

q1 = 10^-4 C …………..B

The instantaneous charge on the capacitor as the capacitor discharges through the inductor ➔ q2

q2 = q1cos (ωt)➔ \(\frac {q_2}{q_2}\) = cos (ωt) ………………..A

Also, q2 = C × V2 = 5 × 10^-6 × 10 …………………….2

q2 = 0.5 × 10^-4 C

From 1 and 2 ➔ \(\frac {q_2}{q_2} = \frac {V_2}{V_1}\) ➔ \(\frac {q_2}{q_2}\) = 0.5 = \(\frac {1}{2}\)

From equation A, we can equate as follows ➔ cos (ωt) = \(\frac {1}{2}\)

ωt = \(\frac {\pi }{2}\) rad ………………..3

For an LC circuit ➔ ω=\(\frac {1}{\sqrt {LC}}\)

ω=20000\(\frac {rad}{s}\) …………………….4

The current through the circuit is given as:

Current (I)=-\(\frac {dq}{dt}\)

Charge decreases with RESPECT to time, so, \(\frac {dq}{dt}\) obtained will be negative and this is why we add a negative sign to MAKE a current positive.

Current = q1 ω sinωt

Considering 3, 4 and B

Current = 10^-4 × 20000 × sin (\(\frac {\pi }{2}\))

Current = 2 A[Sin(\(\frac {\pi }{2}\)) = 1]

Therefore, the current flowing through the circuit is 2 A.

The CORRECT CHOICE is (d) 50 Ω

The explanation is: XL = 2πfL

XL = 2π × 50 × \((\FRAC {20}{\pi })\) = 2000 Ω.

XC = \(\frac {1}{2πfC}\)

XC = 2000 Ω.

Z = √(R^2 + (XL – XC)^2

Z = √50^2 + (2000 – 2000)^2

Z = 50 Ω.

The correct option is (a) 12 A

For EXPLANATION I would say: R = \(\frac {V}{I} = \frac {6}{12}\) = 0.5 Ω.

Impedance = Z = R = 0.5 Ω,

IRMS = \(\frac {E_{RMS}}{Z}\)

Irms = \(\frac {6}{0.5}\)

Irms = 12 A.

Correct answer is (B) Current and voltage

For EXPLANATION I would say: Phasors represent alternating current and voltage of same frequency as vectors in a phasor DIAGRAM with the phase angle between them. Phasors can also be APPLIED to impedance as well as other related complex quantities that are not dependent on time.

Right option is (b) \(\frac {I}{4}\)

For explanation I would say: Electric field between the plates is GIVEN as:

E=\(\frac {q}{A\varepsilon_o}=\frac {It}{A\varepsilon_o}\)

So, the electric FLUX through the area \(\frac {A}{4}\) is given by:

ΦE=\((\frac {A}{4})\)E=\(\frac {It}{4\varepsilon_o}\)

Then the displacement CURRENT will be:

ID = εo\(\frac {d\Phi_E}{dt}\)

ID = εo\(\frac {d}{dt} (\frac {It}{4\epsilon_o})=\frac {I}{4}\)

Therefore, the displacement current through this area is \(\frac {I}{4}\).

Right option is (b) 70.71 V

The BEST EXPLANATION: E = E0 sinωt.

ERMS = \(\FRAC {E_0}{\sqrt {2}}\)

Erms = \(\frac {100}{\sqrt {2}}\)

Erms = 70.71 V

Correct answer is (a) Radio transmitters

For explanation I would say: The most COMMON application of LC oscillators is radio transmitters and RECEIVERS. LC oscillators have good phase noise characteristics as WELL as offer ease of implementation. Due to these FACTORS, LC oscillators are most commonly used in radio-frequency circuits.

Correct choice is (b) False

The explanation: No, this statement is false. Power factor is also DEFINED as the ratio of the resistance to the IMPEDANCE of an AC CIRCUIT. Impedance is the effective resistance of an electric circuit or component to ALTERNATING current. So, both are resistance quantities. Therefore, the ratio between them will be 1, and hence power factor is a UNIT less and dimensionless quantity.

The CORRECT choice is (a) 24 V

For explanation: Given: Ns = 20; Np = 100; VP = 120 V

For a step-down transformer ➔ \(\frac {N_s}{N_p} = \frac {V_s}{V_p}\)

Vs=\(\frac {N_s \times V_P}{N_p}\)

Vs=\(\frac {20 \times 120}{100}\)

Vs=24 V

Therefore, the voltage output from the SECONDARY coil is 24 V.

Correct option is (b) False

The best explanation: Xc = \(\FRAC {1}{\omega_C}\)

Xc = \(\frac {1}{2πfC}\).

THUS the capacitive reactance varies INVERSELY with the frequency. Therefore as frequency INCREASES, the capacitive reactance decreases.

The CORRECT ANSWER is (c) 0.314 V

Explanation: The maximum VOLTAGE generated in the coil,

e0 = nBAω

e0 = NBA × (2πv)

e0 = 100 × 0.01 × 0.1 × 2π × 0.5

e0 = 0.314 V

Right answer is (b) FALSE

Easy EXPLANATION: No, this statement is false. The inductive reactance for an ac circuit containing only an inductor is XL = ωL.

XL = ωL

XL = 2π F L

Correct option is (b) k > 1; VS > Vp, Is < Ip, NS > NP

The explanation: For a step-up transformer, the voltage at the second terminal is greater than the primary terminal, i.e. ➔ Vs > Vp. Similarly, the current in the secondary coil is lesser than that current flowing the primary coil, i.e. ➔ Is < Ip. ALSO, the number of turns in the secondary winding is greater than that in the primary winding, i.e. ➔ Ns > Np. So the transformation RATIO will be greater than 1. So, the correct combination is given as:

k > 1; Vs > Vp, Is < Ip, Ns > Np

Right answer is (c) 8.22 × 10^3J

To explain: We know that, Pav=Vrms Irmscos⁡Φ ………1 and cosΦ;=\(\frac {R}{Z}\) …………………2

In LCR, cosΦ=\(\frac {V_R}{V}=\frac {IR}{IZ}\)and Irms = \( \frac {V_{rms}}{Z}\) ………………….3

 Substituting 2 and 3 in 1

Pav=\(\frac {V_{rms} \big ( \frac {V_rms}{Z} \big )R}{Z}\)

Pav=\(\frac {V_{rms}^2R}{Z^2}\)

Given: Vrms = 24 V; Resistance (R) = 70 Ω; Inductance (I) = 30 mH = 20 × 10^-3 H; Capacitance (C) = 300 μF

XL=2πυL=2π (60)(30 × 10^-3)

XL=11.304 Ω

XC=\(\frac {1}{2\pi υC}=\frac {1}{2\pi (60)(300 \times 10^{-6})}\)

XC=8.846 Ω

For series LCR circuit➔Z=\(\SQRT {R^2+(X_L-X_C)^2}\)

Z=\(\sqrt {70^2+(11.304-8.846)^2}\)

Z=70.04 ≈ 70 Ω

So, the ENERGY USED in 1000 seconds is ➔ Pavt=\((\frac {V_{rms}^2R}{Z^2})\)t

Pavt=\(\frac {24^2 \times 70}{70^2}\) × 1000 =8.22 × 10^3J

Therefore, the energy dissipated in the circuit at 1000 seconds is 8.22 × 10^3J.

Correct answer is (a) True

Easy explanation: Yes, MAXWELL MODIFIED Ampere’s Law. Ampere’s law is true just for steady currents. Maxwell found the shortcoming in Ampere’s law and he modified Ampere’s law to incorporate time-varying electric fields. Maxwell was the one responsible for the correction of the Ampere’s circuital law by the addition of DISPLACEMENT current. He said that we’ve to think about not only the present existing outside the CAPACITOR but also the present referred to as displacement current that existed between the PLATES of the capacitor.

The correct option is (d) k < 1; Vs < Vp, Is > Ip, Ns < Np

The EXPLANATION is: For a step-down transformer, the voltage at the second terminal is lesser than the primary terminal, i.e. ➔ Vs < Vp. Similarly, the NUMBER of turns in the secondary WINDING is lesser than that in the primary winding, i.e. ➔ Ns < Np. Also, the current in the secondary COIL is greater than that current flowing the primary coil, i.e. ➔ Is > Ip. So the TRANSFORMATION ratio will be lesser than 1. So, the correct combination is given as:

k < 1; Vs < Vp, Is > Ip, Ns < Np

The correct answer is (b) cosΦ=\(\FRAC {True \, power}{Apparent \, power}\)

The best I can explain: The power factor of an AC electrical power system is defined as the RATIO of the real or true power ABSORBED by the load to the apparent power flowing in the circuit, and in the closed interval of −1 to 1. The expression for power factor is given as:

cos⁡Φ=\(\frac {True \, power}{Apparent \, power}\)

Correct answer is (C) HALVED

For EXPLANATION I would say: When the frequency is doubled, the capacitive reactance will be halved. This is because the capacitive reactance (Xc) is inversely PROPORTIONAL to the frequency (F). This is the effect of capacitive reactance on frequency.

Right choice is (b) FALSE

For EXPLANATION I would say: No, this statement is false. Phasors rotate in the anti-clockwise direction. Even THOUGH phasors are vectors, they REPRESENT scalar quantities such as voltage and current. It rotates about the origin with an angular speed ω. With the help of a phasor, we can EASILY detect whether one of two quantities are in the same phase or not.

The correct answer is (a) Displacement current

To ELABORATE: Displacement current (ID) is the ELECTRIC current that flows in the gap between the PLATES of the capacitor during its charging, which originates due to the time-varying electric field in the space between the two plates of the capacitor. The expression for displacement current is given as:

ID = εo \(\FRAC {d\Phi_{\varepsilon}}{dt}\)

The CORRECT choice is (a) 67 Ω

The explanation is: \(\FRAC {X_C^{’}}{X_C} =\frac {F}{f^{’}}\)

Xc = \(\frac {(50 \TIMES 200)}{(150)}\)

Xc = 66.7 Ω ≈ 67 Ω

Therefore, the reactance at 150 Hz will be 67 Ω.