Grade 12 : Physics - Alternating Current (Set 4)

Question 1

A sinusoidal alternating voltage source connected across a domestic power line has a peak voltage of $V_0 = 311 ext{ V}$.

What is the root-mean-square (RMS) voltage $V_{rms}$ of this supply?

Accepted Answer

A) 220 V

Answer

B) 311 V

Answer

C) 440 V

Answer

D) 155.5 V

Question 2

An ideal inductor with inductance $L = \frac{0.1}{\pi} ext{ H}$ is connected to a standard 50 Hz AC power source.

Calculate the inductive reactance $X_L$ of the inductor.

Accepted Answer

B) $10	ext{ }\Omega$

Answer

A) $5	ext{ }\Omega$

Answer

C) $20	ext{ }\Omega$

Answer

D) $50	ext{ }\Omega$

Question 3

A capacitor of capacitance $C = \frac{100}{\pi} ext{ }\mu ext{F}$ is connected to an AC source operating at frequency $f = 50 ext{ Hz}$.

What is the capacitive reactance $X_C$ of the capacitor?

Accepted Answer

C) $100	ext{ }\Omega$

Answer

A) $10	ext{ }\Omega$

Answer

B) $50	ext{ }\Omega$

Answer

D) $200	ext{ }\Omega$

Question 4

Circuit Parameters: Resistance $R = 30 ext{ }\Omega$, Inductive Reactance $X_L = 80 ext{ }\Omega$, Capacitive Reactance $X_C = 40 ext{ }\Omega$.

Calculate the total impedance $Z$ of this series RLC circuit.

Accepted Answer

A) $50	ext{ }\Omega$

Answer

B) $70	ext{ }\Omega$

Answer

C) $110	ext{ }\Omega$

Answer

D) $150	ext{ }\Omega$

Question 5

A series resonant circuit contains an inductor $L = 0.25 ext{ H}$ and a capacitor $C = 4 ext{ }\mu ext{F}$.

What is the resonant frequency $f_r$ of the circuit?

Accepted Answer

D) $\frac{500}{\pi}	ext{ Hz}$

Answer

A) $\frac{100}{\pi}	ext{ Hz}$

Answer

B) $\frac{250}{\pi}	ext{ Hz}$

Answer

C) $\frac{1000}{\pi}	ext{ Hz}$

Question 6

A series LCR circuit has an inductor $L = 2.0 ext{ H}$, capacitor $C = 32 ext{ }\mu ext{F}$, and resistor $R = 10 ext{ }\Omega$.

Determine the Quality Factor ($Q$-factor) of the resonant circuit.

Accepted Answer

B) 25

Answer

A) 10

Answer

C) 50

Answer

D) 100

Question 7

Statement I: At resonance, inductive reactance equals capacitive reactance ($X_L = X_C$).
Statement II: The total impedance of a series LCR circuit at resonance equals the resistance $R$.

What is the power factor $\cos\phi$ of a series LCR circuit at resonance?

Accepted Answer

A) 1.0

Answer

B) 0.5

Answer

C) 0.0

Answer

D) 0.707

Question 8

An AC voltage given by $V(t) = 100\sqrt{2} \sin(100\pi t) ext{ V}$ is applied across a purely resistive element $R = 20 ext{ }\Omega$.

Find the average power dissipated in the resistor.

Accepted Answer

C) 500 W

Answer

A) 100 W

Answer

B) 500 W

Answer

D) 250 W

Question 9

An AC circuit carries an RMS current $I_{rms} = 10 ext{ A}$ with a phase difference of $\phi = 30^\circ$ relative to the applied voltage.

What is the reactive (wattless) component of the RMS current?

Accepted Answer

B) 5 A

Answer

A) 10 A

Answer

C) $5\sqrt{3}	ext{ A}$

Answer

D) 0 A

Question 10

A pure capacitor is connected directly across an alternating voltage source $V = V_0 \sin(\omega t)$.

Which phase relationship correctly describes the alternating current $I(t)$ relative to voltage $V(t)$?

Accepted Answer

A) Current leads voltage by $\pi/2$

Answer

B) Current lags voltage by $\pi/2$

Answer

C) Current and voltage are in phase

Answer

D) Current lags voltage by $\pi$

Question 11

A step-down transformer reduces voltage from 2200 V to 220 V. The primary winding contains 4000 turns.

How many turns are in the secondary winding assuming ideal conditions?

Accepted Answer

D) 400

Answer

A) 40

Answer

B) 200

Answer

C) 800

Question 12

A transformer has an efficiency of 90%. It draws power at 200 V with a primary current of 5 A.

Calculate the output electrical power delivered by the transformer.

Accepted Answer

C) 900 W

Answer

A) 1000 W

Answer

B) 800 W

Answer

D) 1111 W

Question 13

AC Generator setup: $N = 100$ turns, Area $A = 0.1m^2$, Angular velocity $\omega = 50 ext{ rad/s}$, Magnetic field $B = 0.2 ext{ T}$.

What is the peak induced electromotive force ($e_0$) generated by the coil?

Accepted Answer

B) 100 V

Answer

A) 50 V

Answer

C) 200 V

Answer

D) 10 V

Question 14

In an LC circuit undergoing un-damped oscillations, maximum charge stored in the capacitor is $Q_0 = 4 ext{ }\mu ext{C}$ and total stored energy is $E = 8 ext{ }\mu ext{J}$.

What is the capacitance $C$ of the capacitor?

Accepted Answer

A) $1.0	ext{ }\mu	ext{F}$

Answer

B) $2.0	ext{ }\mu	ext{F}$

Answer

C) $0.5	ext{ }\mu	ext{F}$

Answer

D) $4.0	ext{ }\mu	ext{F}$

Question 15

A series RC circuit consists of a resistor $R = 40 ext{ }\Omega$ and capacitive reactance $X_C = 30 ext{ }\Omega$.

Determine the magnitude of phase angle $\phi$ and phase relationship of current relative to voltage.

Accepted Answer

D) Current leads voltage by $37^\circ$

Answer

A) Current lags voltage by $53^\circ$

Answer

B) Current leads voltage by $53^\circ$

Answer

C) Current lags voltage by $37^\circ$

Question 16

A choke coil is used to limit alternating current in a circuit with minimal power loss.

What physical properties must an effective choke coil possess?

Accepted Answer

B) High inductance and low resistance

Answer

A) Low inductance and high resistance

Answer

C) High inductance and high resistance

Answer

D) Low inductance and low resistance

Question 17

A resonant series LCR circuit has inductance $L = 10 ext{ mH}$ and resistance $R = 5 ext{ }\Omega$.

Find the bandwidth $\Delta \omega$ of the resonant curve.

Accepted Answer

A) 500 rad/s

Answer

B) 250 rad/s

Answer

C) 1000 rad/s

Answer

D) 50 rad/s

Question 18

An instantaneous AC voltage $V(t) = 200\sqrt{2} \sin(100 t) ext{ V}$ is applied across a pure inductor of $L = 2 ext{ H}$.

Which equation represents the instantaneous current $I(t)$?

Accepted Answer

C) $I(t) = \sqrt{2} \sin(100t - \pi/2)	ext{ A}$

Answer

A) $I(t) = \sqrt{2} \sin(100t + \pi/2)	ext{ A}$

Answer

B) $I(t) = 200 \sin(100t)	ext{ A}$

Answer

D) $I(t) = 100\sqrt{2} \sin(100t - \pi/2)	ext{ A}$

Question 19

An ideal transformer receives $V_p = 220 ext{ V}$ and delivers output at $V_s = 11 ext{ V}$. Primary current is $I_p = 2 ext{ A}$.

Calculate the secondary current $I_s$.

Accepted Answer

B) 40 A

Answer

A) 20 A

Answer

C) 0.1 A

Answer

D) 440 A

Question 20

In a series LCR circuit, inductive reactance $X_L$ is greater than capacitive reactance $X_C$.

How does the total current relate in phase to the applied source voltage?

Accepted Answer

A) Current lags behind applied voltage

Answer

B) Current leads ahead of applied voltage

Answer

C) Current is exactly in phase with voltage

Answer

D) Phase angle is $180^\circ$