Grade 12 : Physics - Alternating Current (Set 3)

Question 1

An alternating voltage source is described by the equation $v = 282 \sin(100\pi t) ext{ V}$. What are the RMS voltage and the frequency of the source? (Use $\sqrt{2} \approx 1.41$)

Accepted Answer

A) $200	ext{ V}, 50	ext{ Hz}$

Answer

B) $282	ext{ V}, 100	ext{ Hz}$

Answer

C) $141	ext{ V}, 50	ext{ Hz}$

Answer

D) $200	ext{ V}, 100	ext{ Hz}$

Question 2

An ideal inductor of inductance 0.2 H is connected across an AC supply given by $v = 141 \sin(100\pi t) ext{ V}$. What is the RMS current flowing through the inductor?

Accepted Answer

B) 1.59 A

Answer

A) 0.50 A

Answer

C) 2.25 A

Answer

D) 3.18 A

Question 3

A capacitor of capacitance $C = \frac{100}{\pi}\ \mu ext{F}$ is connected to a $220 ext{ V}, 50 ext{ Hz}$ AC power supply. What is the capacitive reactance $X_C$ of the circuit?

Accepted Answer

B) $100\ \Omega$

Answer

A) $50\ \Omega$

Answer

C) $200\ \Omega$

Answer

D) $314\ \Omega$

Question 4

In a series LCR circuit, $R = 30\ \Omega$, $X_L = 80\ \Omega$, and $X_C = 40\ \Omega$. Calculate the total impedance $Z$ and the power factor $\cos\phi$ of the circuit.

Accepted Answer

A) $50\ \Omega,\ 0.60$

Answer

B) $70\ \Omega,\ 0.80$

Answer

C) $50\ \Omega,\ 0.80$

Answer

D) $90\ \Omega,\ 0.60$

Question 5

A series LCR circuit consists of an inductor $L = 0.1 ext{ H}$, a capacitor $C = 10\ \mu ext{F}$, and a resistor $R = 20\ \Omega$. What is the resonant angular frequency $\omega_0$ of the circuit?

Accepted Answer

C) 1000 rad/s

Answer

A) 100 rad/s

Answer

B) 500 rad/s

Answer

D) 2000 rad/s

Question 6

A series resonant LCR circuit has an inductance $L = 2 ext{ H}$, capacitance $C = 2\ \mu ext{F}$, and resistance $R = 20\ \Omega$. Determine the Quality factor ($Q$-factor) of the circuit.

Accepted Answer

B) 50

Answer

A) 25

Answer

C) 100

Answer

D) 200

Question 7

An AC voltage of $V_{rms} = 200 ext{ V}$ is applied to a series circuit with resistance $R = 40\ \Omega$ and total reactance $X = 30\ \Omega$. Find the average power dissipated in the circuit.

Accepted Answer

B) 640 W

Answer

A) 400 W

Answer

C) 800 W

Answer

D) 1000 W

Question 8

A series AC circuit carries an RMS current of 5 A. If the phase angle between voltage and current is $60^\circ$, what is the magnitude of the wattless current?

Accepted Answer

B) 4.33 A

Answer

A) 2.50 A

Answer

C) 5.00 A

Answer

D) 1.25 A

Question 9

In a series LCR circuit, what is the phase difference between the voltage across the inductor ($V_L$) and the voltage across the capacitor ($V_C$)?

Accepted Answer

D) $180^\circ$

Answer

A) $0^\circ$

Answer

B) $45^\circ$

Answer

C) $90^\circ$

Question 10

An ideal step-down transformer reduces 2200 V primary voltage to 220 V secondary voltage. If the primary coil has 2000 turns and secondary output power is 4.4 kW, find the number of turns in the secondary coil and the primary current.

Accepted Answer

A) $200	ext{ turns, } 2	ext{ A}$

Answer

B) $200	ext{ turns, } 20	ext{ A}$

Answer

C) $100	ext{ turns, } 2	ext{ A}$

Answer

D) $400	ext{ turns, } 4	ext{ A}$

Question 11

An LC circuit consists of a 10 mH inductor and a $1\ \mu ext{F}$ capacitor initially charged to 50 V. What is the maximum current that flows through the inductor during LC oscillations?

Accepted Answer

C) 0.50 A

Answer

A) 0.10 A

Answer

B) 0.25 A

Answer

D) 1.00 A

Question 12

The bandwidth of a series LCR resonant circuit is 100 rad/s. If the inductance of the circuit is $L = 0.2 ext{ H}$, what is the resistance $R$ of the circuit?

Accepted Answer

C) $20\ \Omega$

Answer

A) $5\ \Omega$

Answer

B) $10\ \Omega$

Answer

D) $50\ \Omega$

Question 13

A direct current of 3 A is combined with an alternating current $i = 4 \sin(\omega t) ext{ A}$ in a resistor. What will be the reading on a hot-wire ammeter connected in this circuit?

Accepted Answer

A) 4.12 A

Answer

B) 5.00 A

Answer

C) 7.00 A

Answer

D) 3.50 A

Question 14

A choke coil has an inductance of 0.4 H and a resistance of $2\ \Omega$. It is connected to a $110 ext{ V}, 50 ext{ Hz}$ AC line. What is the approximate phase angle $\phi$ between voltage and current?

Accepted Answer

C) $89.1^\circ$

Answer

A) $0^\circ$

Answer

B) $45^\circ$

Answer

D) $60^\circ$

Question 15

In a series LCR circuit, resonance is achieved at a frequency $f_0$. If the capacitance of the capacitor is increased by a factor of 4 while keeping inductance constant, how does the new resonant frequency $f_0'$ compare to $f_0$?

Accepted Answer

C) It is halved ($f_0 / 2$)

Answer

A) It doubles ($2 f_0$)

Answer

B) It quadruples ($4 f_0$)

Answer

D) It remains unchanged

Question 16

An alternating voltage $v = 100 \sin(100 t) ext{ V}$ is applied across a pure capacitor of capacitance $C = 50\ \mu ext{F}$. Which expression correctly represents the instantaneous current $i(t)$?

Accepted Answer

B) $i(t) = 0.5 \sin(100 t + \pi/2)	ext{ A}$

Answer

A) $i(t) = 0.5 \sin(100 t - \pi/2)	ext{ A}$

Answer

C) $i(t) = 2.0 \sin(100 t + \pi/2)	ext{ A}$

Answer

D) $i(t) = 0.5 \sin(100 t)	ext{ A}$

Question 17

A transformer operates with an efficiency of 90%. It receives an input power of 3 kW at 200 V. If the output voltage at the secondary coil is 600 V, what is the secondary current?

Accepted Answer

C) 4.5 A

Answer

A) 15.0 A

Answer

B) 5.0 A

Answer

D) 3.0 A

Question 18

In a series LCR circuit, voltmeters connected across the resistor, inductor, and capacitor read $V_R = 40 ext{ V}$, $V_L = 70 ext{ V}$, and $V_C = 40 ext{ V}$ respectively. What is the RMS voltage of the main AC power source?

Accepted Answer

D) 50 V

Answer

A) 150 V

Answer

B) 110 V

Answer

C) 70 V

Question 19

A resistor of $12\ \Omega$ and an inductor of inductive reactance $16\ \Omega$ are connected in series across a 100 V RMS AC supply. What is the average power dissipated in the inductor alone?

Accepted Answer

A) 0 W

Answer

B) 300 W

Answer

C) 400 W

Answer

D) 432 W

Question 20

Circuit	R ($\Omega$)	$X_L$ ($\Omega$)	$X_C$ ($\Omega$)
Circuit 1	10	20	20
Circuit 2	15	30	10
Circuit 3	20	10	40
Circuit 4	0	25	25

Based on the table above, which circuit operates at electrical resonance and presents a non-zero finite impedance to the AC supply?

Accepted Answer

A) Circuit 1

Answer

B) Circuit 2

Answer

C) Circuit 3

Answer

D) Circuit 4