DC Pandey Solutions (JEE Main): Alternating Current | DC Pandey Solutions for JEE Physics PDF Download

 Page 1


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
Q 1.  (a) What is the reactance of a 2.00 H inductor at a frequency of 50.0 Hz? 
  (b) What is the inductance of an inductor whose reactance is 2.00 ?
 
at 50.0 Hz? 
  (c) What is the reactance of a 2.00 ?F
 
capacitor at a frequency of 50.0 Hz? 
  (d) What is the capacitance of a capacitor whose reactance is 2.00 ? at 50.0 Hz? 
Q 2.  A 300 ? resistor, a 0.250 H inductor, and a 8.00 ?F
 
capacitor are in series with an ac source with 
voltage amplitude 120 V and angular frequency 400 rad/s. 
  (a) What is the current amplitude? 
(b) What is the phase angle of the source voltage with respect to the current? Does the source 
voltage lag or lead the current? 
  (c) What are the voltage amplitudes across the resistor, inductor, and capacitor? 
Q 3.  In an L-C-R series circuit, R = 150 ?, L = 0.750 H, and C = 0.0180 ?F.
 
The source has voltage 
amplitude V = 150 V and a frequency equal to the resonance frequency of the circuit. 
  (a) What is the power factor? 
  (b) What is the average power delivered by the source? 
(c) The capacitor is replaced by one with C = 0.0360 ?B and the source frequency is adjusted to 
the new resonance value. Then, what is the average power delivered by the source? 
Q 4.  A series circuit has an impedance of 60.0 ? and a power factor of 0.720 at 50.0 Hz. The source 
voltage lags the current. 
(a) What circuit element, an inductor or a capacitor, should be placed in series with the circuit to 
raise its power factor? 
  (b) What size element will raise the power factor to unity? 
Q 5.  Voltage and current for a circuit with two elements in series are expressed as : 
    V(t) = 170sin(6280t + ?/3) volt  
    i(t) = 8.5sin(6280t + ?/2)amp  
  (a) Plot the two waveforms. 
  (b) Determine the frequency in Hz. 
  (c) Determine the power factor stating its nature. 
  (d) What are the values of the elements? 
Q 6.  A 5.00 H inductor with negligible resistance is connected across an ac source. Voltage amplitude 
is kept constant at 60.0 V but whose frequency can be varied. Find the current amplitude when the 
angular, frequency is 
  (a) 100 rad/s (b) 1000 rad/s (c) 10000 rad/s 
Q 7.  A 300 ?
 
resistor is connected in series with a 0.800 H inductor. The voltage across the resistor as a 
function of time is V
R
 = (2.50 V)cos [(950rad/s)t]. 
  (a) Derive an expression for the circuit current. 
  (b) Determine the inductive reactance of the inductor. 
  (c) Derive an expression for the voltage V
L
 across the inductor. 
Q 8.  An L-C-R series circuit with L = 0.120 H, R = 240 ?, and C = 7.30 ?F
 
carries an rms current of 
0.450 A with a frequency of 400 Hz. 
  (a) What are the phase angle and power factor for this circuit? 
Page 2


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
Q 1.  (a) What is the reactance of a 2.00 H inductor at a frequency of 50.0 Hz? 
  (b) What is the inductance of an inductor whose reactance is 2.00 ?
 
at 50.0 Hz? 
  (c) What is the reactance of a 2.00 ?F
 
capacitor at a frequency of 50.0 Hz? 
  (d) What is the capacitance of a capacitor whose reactance is 2.00 ? at 50.0 Hz? 
Q 2.  A 300 ? resistor, a 0.250 H inductor, and a 8.00 ?F
 
capacitor are in series with an ac source with 
voltage amplitude 120 V and angular frequency 400 rad/s. 
  (a) What is the current amplitude? 
(b) What is the phase angle of the source voltage with respect to the current? Does the source 
voltage lag or lead the current? 
  (c) What are the voltage amplitudes across the resistor, inductor, and capacitor? 
Q 3.  In an L-C-R series circuit, R = 150 ?, L = 0.750 H, and C = 0.0180 ?F.
 
The source has voltage 
amplitude V = 150 V and a frequency equal to the resonance frequency of the circuit. 
  (a) What is the power factor? 
  (b) What is the average power delivered by the source? 
(c) The capacitor is replaced by one with C = 0.0360 ?B and the source frequency is adjusted to 
the new resonance value. Then, what is the average power delivered by the source? 
Q 4.  A series circuit has an impedance of 60.0 ? and a power factor of 0.720 at 50.0 Hz. The source 
voltage lags the current. 
(a) What circuit element, an inductor or a capacitor, should be placed in series with the circuit to 
raise its power factor? 
  (b) What size element will raise the power factor to unity? 
Q 5.  Voltage and current for a circuit with two elements in series are expressed as : 
    V(t) = 170sin(6280t + ?/3) volt  
    i(t) = 8.5sin(6280t + ?/2)amp  
  (a) Plot the two waveforms. 
  (b) Determine the frequency in Hz. 
  (c) Determine the power factor stating its nature. 
  (d) What are the values of the elements? 
Q 6.  A 5.00 H inductor with negligible resistance is connected across an ac source. Voltage amplitude 
is kept constant at 60.0 V but whose frequency can be varied. Find the current amplitude when the 
angular, frequency is 
  (a) 100 rad/s (b) 1000 rad/s (c) 10000 rad/s 
Q 7.  A 300 ?
 
resistor is connected in series with a 0.800 H inductor. The voltage across the resistor as a 
function of time is V
R
 = (2.50 V)cos [(950rad/s)t]. 
  (a) Derive an expression for the circuit current. 
  (b) Determine the inductive reactance of the inductor. 
  (c) Derive an expression for the voltage V
L
 across the inductor. 
Q 8.  An L-C-R series circuit with L = 0.120 H, R = 240 ?, and C = 7.30 ?F
 
carries an rms current of 
0.450 A with a frequency of 400 Hz. 
  (a) What are the phase angle and power factor for this circuit? 
  (b) What is the impedance of the circuit? 
  (c) What is the rms voltage of the source? 
  (d) What average power is delivered by the source? 
(e) What is the average rate at which electrical energy is converted to thermal energy in the 
resistor? 
(f) What is the average rate at which electrical energy is dissipated ( converted to other forms) in 
the capacitor? 
(g) In the inductor? 
Solutions 
1.  (a)X
L
 =2?fL 
   (b) 
  (c)   
  (d) 
2.  X
L
 = ?L = 100 ?  
    
    
  (a) 
  (b) Since X
C
 > X
L
, voltage lags the current by an angle given by 
    
  (c) (V
0
)
R
 = I
0
R = (0.326) 300 = 97.8 V  
   (V
0
)
L
 = I
0
X
L
 = (0.326) (100) = 32.6 V  
   (V
0
)
C
 = I
0
X
C
 = (0.326) (312.5) = 102 V 
3.  (a) At resonance frequency, X
L
= X
C
, Z = R and power factor 
    
  (b)   
  (c) Again P = = 75 W  
4.  (a) Voltage lags 
   X
C
 > X
L
 
  Power factor, 
    
  To increase the power factor denominator should decrease.  
Hence X
L
 should increase. Therefore an inductor is required to be connected. 
  (b) 
   R = 0.72 Z = 0.72 × 60 = 43.2 ?  
   {X
C 
- X
L
) 
Page 3


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
Q 1.  (a) What is the reactance of a 2.00 H inductor at a frequency of 50.0 Hz? 
  (b) What is the inductance of an inductor whose reactance is 2.00 ?
 
at 50.0 Hz? 
  (c) What is the reactance of a 2.00 ?F
 
capacitor at a frequency of 50.0 Hz? 
  (d) What is the capacitance of a capacitor whose reactance is 2.00 ? at 50.0 Hz? 
Q 2.  A 300 ? resistor, a 0.250 H inductor, and a 8.00 ?F
 
capacitor are in series with an ac source with 
voltage amplitude 120 V and angular frequency 400 rad/s. 
  (a) What is the current amplitude? 
(b) What is the phase angle of the source voltage with respect to the current? Does the source 
voltage lag or lead the current? 
  (c) What are the voltage amplitudes across the resistor, inductor, and capacitor? 
Q 3.  In an L-C-R series circuit, R = 150 ?, L = 0.750 H, and C = 0.0180 ?F.
 
The source has voltage 
amplitude V = 150 V and a frequency equal to the resonance frequency of the circuit. 
  (a) What is the power factor? 
  (b) What is the average power delivered by the source? 
(c) The capacitor is replaced by one with C = 0.0360 ?B and the source frequency is adjusted to 
the new resonance value. Then, what is the average power delivered by the source? 
Q 4.  A series circuit has an impedance of 60.0 ? and a power factor of 0.720 at 50.0 Hz. The source 
voltage lags the current. 
(a) What circuit element, an inductor or a capacitor, should be placed in series with the circuit to 
raise its power factor? 
  (b) What size element will raise the power factor to unity? 
Q 5.  Voltage and current for a circuit with two elements in series are expressed as : 
    V(t) = 170sin(6280t + ?/3) volt  
    i(t) = 8.5sin(6280t + ?/2)amp  
  (a) Plot the two waveforms. 
  (b) Determine the frequency in Hz. 
  (c) Determine the power factor stating its nature. 
  (d) What are the values of the elements? 
Q 6.  A 5.00 H inductor with negligible resistance is connected across an ac source. Voltage amplitude 
is kept constant at 60.0 V but whose frequency can be varied. Find the current amplitude when the 
angular, frequency is 
  (a) 100 rad/s (b) 1000 rad/s (c) 10000 rad/s 
Q 7.  A 300 ?
 
resistor is connected in series with a 0.800 H inductor. The voltage across the resistor as a 
function of time is V
R
 = (2.50 V)cos [(950rad/s)t]. 
  (a) Derive an expression for the circuit current. 
  (b) Determine the inductive reactance of the inductor. 
  (c) Derive an expression for the voltage V
L
 across the inductor. 
Q 8.  An L-C-R series circuit with L = 0.120 H, R = 240 ?, and C = 7.30 ?F
 
carries an rms current of 
0.450 A with a frequency of 400 Hz. 
  (a) What are the phase angle and power factor for this circuit? 
  (b) What is the impedance of the circuit? 
  (c) What is the rms voltage of the source? 
  (d) What average power is delivered by the source? 
(e) What is the average rate at which electrical energy is converted to thermal energy in the 
resistor? 
(f) What is the average rate at which electrical energy is dissipated ( converted to other forms) in 
the capacitor? 
(g) In the inductor? 
Solutions 
1.  (a)X
L
 =2?fL 
   (b) 
  (c)   
  (d) 
2.  X
L
 = ?L = 100 ?  
    
    
  (a) 
  (b) Since X
C
 > X
L
, voltage lags the current by an angle given by 
    
  (c) (V
0
)
R
 = I
0
R = (0.326) 300 = 97.8 V  
   (V
0
)
L
 = I
0
X
L
 = (0.326) (100) = 32.6 V  
   (V
0
)
C
 = I
0
X
C
 = (0.326) (312.5) = 102 V 
3.  (a) At resonance frequency, X
L
= X
C
, Z = R and power factor 
    
  (b)   
  (c) Again P = = 75 W  
4.  (a) Voltage lags 
   X
C
 > X
L
 
  Power factor, 
    
  To increase the power factor denominator should decrease.  
Hence X
L
 should increase. Therefore an inductor is required to be connected. 
  (b) 
   R = 0.72 Z = 0.72 × 60 = 43.2 ?  
   {X
C 
- X
L
) 
  New inductor of inductance 41.64 ? should be added in the circuit. 
    
5.  (b) 
  (c) 
   Power factor = cos ? = cos 30° 
    
  From the given functions of V and i we can see that current function leads the voltage function. 
  (d) 
   
    
   = 10 ? 
    
   = 15.92 × 10
-6
F 
6.  
7.  (a) A  
   = 8.33 mA 
  Current function and V
R
 function are in phase. Hence, 
   I = (8.33 mA) cos [(950 rad/s) t] 
  (b) X
L
= ?L
 
= 950 × 0.8 = 760 ? 
  (c) (V
0
)
L
 = I
0
X
L
 = (8.33 × 10
-3
) (760) 
   = 6.33V 
  Now, V
L
 function leads the current (or V
R
 ) function by 90°. 
  F
L 
= 6.33 cos(950t + 90°) = - 6.33 sin (950 t) 
8.  X
L
=2 ? fL = 301? 
   X
C
 = = 55? 
   
   = 343?  
  (a)  
    
   = 45.6° 
Page 4


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
Q 1.  (a) What is the reactance of a 2.00 H inductor at a frequency of 50.0 Hz? 
  (b) What is the inductance of an inductor whose reactance is 2.00 ?
 
at 50.0 Hz? 
  (c) What is the reactance of a 2.00 ?F
 
capacitor at a frequency of 50.0 Hz? 
  (d) What is the capacitance of a capacitor whose reactance is 2.00 ? at 50.0 Hz? 
Q 2.  A 300 ? resistor, a 0.250 H inductor, and a 8.00 ?F
 
capacitor are in series with an ac source with 
voltage amplitude 120 V and angular frequency 400 rad/s. 
  (a) What is the current amplitude? 
(b) What is the phase angle of the source voltage with respect to the current? Does the source 
voltage lag or lead the current? 
  (c) What are the voltage amplitudes across the resistor, inductor, and capacitor? 
Q 3.  In an L-C-R series circuit, R = 150 ?, L = 0.750 H, and C = 0.0180 ?F.
 
The source has voltage 
amplitude V = 150 V and a frequency equal to the resonance frequency of the circuit. 
  (a) What is the power factor? 
  (b) What is the average power delivered by the source? 
(c) The capacitor is replaced by one with C = 0.0360 ?B and the source frequency is adjusted to 
the new resonance value. Then, what is the average power delivered by the source? 
Q 4.  A series circuit has an impedance of 60.0 ? and a power factor of 0.720 at 50.0 Hz. The source 
voltage lags the current. 
(a) What circuit element, an inductor or a capacitor, should be placed in series with the circuit to 
raise its power factor? 
  (b) What size element will raise the power factor to unity? 
Q 5.  Voltage and current for a circuit with two elements in series are expressed as : 
    V(t) = 170sin(6280t + ?/3) volt  
    i(t) = 8.5sin(6280t + ?/2)amp  
  (a) Plot the two waveforms. 
  (b) Determine the frequency in Hz. 
  (c) Determine the power factor stating its nature. 
  (d) What are the values of the elements? 
Q 6.  A 5.00 H inductor with negligible resistance is connected across an ac source. Voltage amplitude 
is kept constant at 60.0 V but whose frequency can be varied. Find the current amplitude when the 
angular, frequency is 
  (a) 100 rad/s (b) 1000 rad/s (c) 10000 rad/s 
Q 7.  A 300 ?
 
resistor is connected in series with a 0.800 H inductor. The voltage across the resistor as a 
function of time is V
R
 = (2.50 V)cos [(950rad/s)t]. 
  (a) Derive an expression for the circuit current. 
  (b) Determine the inductive reactance of the inductor. 
  (c) Derive an expression for the voltage V
L
 across the inductor. 
Q 8.  An L-C-R series circuit with L = 0.120 H, R = 240 ?, and C = 7.30 ?F
 
carries an rms current of 
0.450 A with a frequency of 400 Hz. 
  (a) What are the phase angle and power factor for this circuit? 
  (b) What is the impedance of the circuit? 
  (c) What is the rms voltage of the source? 
  (d) What average power is delivered by the source? 
(e) What is the average rate at which electrical energy is converted to thermal energy in the 
resistor? 
(f) What is the average rate at which electrical energy is dissipated ( converted to other forms) in 
the capacitor? 
(g) In the inductor? 
Solutions 
1.  (a)X
L
 =2?fL 
   (b) 
  (c)   
  (d) 
2.  X
L
 = ?L = 100 ?  
    
    
  (a) 
  (b) Since X
C
 > X
L
, voltage lags the current by an angle given by 
    
  (c) (V
0
)
R
 = I
0
R = (0.326) 300 = 97.8 V  
   (V
0
)
L
 = I
0
X
L
 = (0.326) (100) = 32.6 V  
   (V
0
)
C
 = I
0
X
C
 = (0.326) (312.5) = 102 V 
3.  (a) At resonance frequency, X
L
= X
C
, Z = R and power factor 
    
  (b)   
  (c) Again P = = 75 W  
4.  (a) Voltage lags 
   X
C
 > X
L
 
  Power factor, 
    
  To increase the power factor denominator should decrease.  
Hence X
L
 should increase. Therefore an inductor is required to be connected. 
  (b) 
   R = 0.72 Z = 0.72 × 60 = 43.2 ?  
   {X
C 
- X
L
) 
  New inductor of inductance 41.64 ? should be added in the circuit. 
    
5.  (b) 
  (c) 
   Power factor = cos ? = cos 30° 
    
  From the given functions of V and i we can see that current function leads the voltage function. 
  (d) 
   
    
   = 10 ? 
    
   = 15.92 × 10
-6
F 
6.  
7.  (a) A  
   = 8.33 mA 
  Current function and V
R
 function are in phase. Hence, 
   I = (8.33 mA) cos [(950 rad/s) t] 
  (b) X
L
= ?L
 
= 950 × 0.8 = 760 ? 
  (c) (V
0
)
L
 = I
0
X
L
 = (8.33 × 10
-3
) (760) 
   = 6.33V 
  Now, V
L
 function leads the current (or V
R
 ) function by 90°. 
  F
L 
= 6.33 cos(950t + 90°) = - 6.33 sin (950 t) 
8.  X
L
=2 ? fL = 301? 
   X
C
 = = 55? 
   
   = 343?  
  (a)  
    
   = 45.6° 
   
   = 0.699 
  Since X
L
 > X
C
, voltage leads the current.  
  (b) Impedance = Z = 343 ? 
  (c) V
rms
 = I
rms
 Z 
   = 0.45 × 343 = 155 V  
  (d) 
2
rms
P I R ? 
   = (0.45)
2
 (240) = 48.6W  
  (e) P = P
R
= 48.6 W 
  (f) P
C
 = 0  
  (g) P
L 
= 0 
 
Objective Questions 
  Single Correct Option 
Q 1.  The term cos ?
 
in an AC circuit is called 
  (a) form factor  (b) phase factor (c) power factor  (d) quality factor 
Q 2.  A DC ammeter cannot measure alternating current because 
  (a) AC changes its direction   (b) DC instruments will measure the average value 
  (c) AC can damage the DC instrument (d) AC produces more heat 
Q 3.  As the frequency of an alternating current increases the impedance of the circuit 
  (a) increases continuously    (b) decreases continuously 
  (c) remains constant     (d) None of these 
Q 4.  Phaser diagram of a series AC circuit is shown in figure. Then 
 
  (a) The circuit must be containing resistor and capacitor only 
  (b) The circuit must be containing resistor and inductor only 
  (c) The circuit must be containing all three elements L, C and R 
  (d) The circuit cannot have only capacitor and inductor 
Q 5.  The rms value of an alternating current 
  (a) is equal to 0.707 times peak value  (b) is equal to 0.636 times peak value 
  (c) is equal to 2 times the peak value  (d) None of the above 
Q 6.  In an AC circuit the applied potential difference and the current flowing are given by : 
   V = 200 sin 1 00t volt, I = 5 sin 100t
2
? ??
?
??
??
amp 
  The power consumption is equal to 
  (a) 1000 W   (b) 40 W   (c) 20 W   (d) zero  
Q 7.  The impedance of a series L-C-R circuit in an AC circuit is 
(a) 
LC
R (X X ) ?? (b) 
22
LC
R (X X ) ??  (c) R    (d) None of these 
Page 5


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
Q 1.  (a) What is the reactance of a 2.00 H inductor at a frequency of 50.0 Hz? 
  (b) What is the inductance of an inductor whose reactance is 2.00 ?
 
at 50.0 Hz? 
  (c) What is the reactance of a 2.00 ?F
 
capacitor at a frequency of 50.0 Hz? 
  (d) What is the capacitance of a capacitor whose reactance is 2.00 ? at 50.0 Hz? 
Q 2.  A 300 ? resistor, a 0.250 H inductor, and a 8.00 ?F
 
capacitor are in series with an ac source with 
voltage amplitude 120 V and angular frequency 400 rad/s. 
  (a) What is the current amplitude? 
(b) What is the phase angle of the source voltage with respect to the current? Does the source 
voltage lag or lead the current? 
  (c) What are the voltage amplitudes across the resistor, inductor, and capacitor? 
Q 3.  In an L-C-R series circuit, R = 150 ?, L = 0.750 H, and C = 0.0180 ?F.
 
The source has voltage 
amplitude V = 150 V and a frequency equal to the resonance frequency of the circuit. 
  (a) What is the power factor? 
  (b) What is the average power delivered by the source? 
(c) The capacitor is replaced by one with C = 0.0360 ?B and the source frequency is adjusted to 
the new resonance value. Then, what is the average power delivered by the source? 
Q 4.  A series circuit has an impedance of 60.0 ? and a power factor of 0.720 at 50.0 Hz. The source 
voltage lags the current. 
(a) What circuit element, an inductor or a capacitor, should be placed in series with the circuit to 
raise its power factor? 
  (b) What size element will raise the power factor to unity? 
Q 5.  Voltage and current for a circuit with two elements in series are expressed as : 
    V(t) = 170sin(6280t + ?/3) volt  
    i(t) = 8.5sin(6280t + ?/2)amp  
  (a) Plot the two waveforms. 
  (b) Determine the frequency in Hz. 
  (c) Determine the power factor stating its nature. 
  (d) What are the values of the elements? 
Q 6.  A 5.00 H inductor with negligible resistance is connected across an ac source. Voltage amplitude 
is kept constant at 60.0 V but whose frequency can be varied. Find the current amplitude when the 
angular, frequency is 
  (a) 100 rad/s (b) 1000 rad/s (c) 10000 rad/s 
Q 7.  A 300 ?
 
resistor is connected in series with a 0.800 H inductor. The voltage across the resistor as a 
function of time is V
R
 = (2.50 V)cos [(950rad/s)t]. 
  (a) Derive an expression for the circuit current. 
  (b) Determine the inductive reactance of the inductor. 
  (c) Derive an expression for the voltage V
L
 across the inductor. 
Q 8.  An L-C-R series circuit with L = 0.120 H, R = 240 ?, and C = 7.30 ?F
 
carries an rms current of 
0.450 A with a frequency of 400 Hz. 
  (a) What are the phase angle and power factor for this circuit? 
  (b) What is the impedance of the circuit? 
  (c) What is the rms voltage of the source? 
  (d) What average power is delivered by the source? 
(e) What is the average rate at which electrical energy is converted to thermal energy in the 
resistor? 
(f) What is the average rate at which electrical energy is dissipated ( converted to other forms) in 
the capacitor? 
(g) In the inductor? 
Solutions 
1.  (a)X
L
 =2?fL 
   (b) 
  (c)   
  (d) 
2.  X
L
 = ?L = 100 ?  
    
    
  (a) 
  (b) Since X
C
 > X
L
, voltage lags the current by an angle given by 
    
  (c) (V
0
)
R
 = I
0
R = (0.326) 300 = 97.8 V  
   (V
0
)
L
 = I
0
X
L
 = (0.326) (100) = 32.6 V  
   (V
0
)
C
 = I
0
X
C
 = (0.326) (312.5) = 102 V 
3.  (a) At resonance frequency, X
L
= X
C
, Z = R and power factor 
    
  (b)   
  (c) Again P = = 75 W  
4.  (a) Voltage lags 
   X
C
 > X
L
 
  Power factor, 
    
  To increase the power factor denominator should decrease.  
Hence X
L
 should increase. Therefore an inductor is required to be connected. 
  (b) 
   R = 0.72 Z = 0.72 × 60 = 43.2 ?  
   {X
C 
- X
L
) 
  New inductor of inductance 41.64 ? should be added in the circuit. 
    
5.  (b) 
  (c) 
   Power factor = cos ? = cos 30° 
    
  From the given functions of V and i we can see that current function leads the voltage function. 
  (d) 
   
    
   = 10 ? 
    
   = 15.92 × 10
-6
F 
6.  
7.  (a) A  
   = 8.33 mA 
  Current function and V
R
 function are in phase. Hence, 
   I = (8.33 mA) cos [(950 rad/s) t] 
  (b) X
L
= ?L
 
= 950 × 0.8 = 760 ? 
  (c) (V
0
)
L
 = I
0
X
L
 = (8.33 × 10
-3
) (760) 
   = 6.33V 
  Now, V
L
 function leads the current (or V
R
 ) function by 90°. 
  F
L 
= 6.33 cos(950t + 90°) = - 6.33 sin (950 t) 
8.  X
L
=2 ? fL = 301? 
   X
C
 = = 55? 
   
   = 343?  
  (a)  
    
   = 45.6° 
   
   = 0.699 
  Since X
L
 > X
C
, voltage leads the current.  
  (b) Impedance = Z = 343 ? 
  (c) V
rms
 = I
rms
 Z 
   = 0.45 × 343 = 155 V  
  (d) 
2
rms
P I R ? 
   = (0.45)
2
 (240) = 48.6W  
  (e) P = P
R
= 48.6 W 
  (f) P
C
 = 0  
  (g) P
L 
= 0 
 
Objective Questions 
  Single Correct Option 
Q 1.  The term cos ?
 
in an AC circuit is called 
  (a) form factor  (b) phase factor (c) power factor  (d) quality factor 
Q 2.  A DC ammeter cannot measure alternating current because 
  (a) AC changes its direction   (b) DC instruments will measure the average value 
  (c) AC can damage the DC instrument (d) AC produces more heat 
Q 3.  As the frequency of an alternating current increases the impedance of the circuit 
  (a) increases continuously    (b) decreases continuously 
  (c) remains constant     (d) None of these 
Q 4.  Phaser diagram of a series AC circuit is shown in figure. Then 
 
  (a) The circuit must be containing resistor and capacitor only 
  (b) The circuit must be containing resistor and inductor only 
  (c) The circuit must be containing all three elements L, C and R 
  (d) The circuit cannot have only capacitor and inductor 
Q 5.  The rms value of an alternating current 
  (a) is equal to 0.707 times peak value  (b) is equal to 0.636 times peak value 
  (c) is equal to 2 times the peak value  (d) None of the above 
Q 6.  In an AC circuit the applied potential difference and the current flowing are given by : 
   V = 200 sin 1 00t volt, I = 5 sin 100t
2
? ??
?
??
??
amp 
  The power consumption is equal to 
  (a) 1000 W   (b) 40 W   (c) 20 W   (d) zero  
Q 7.  The impedance of a series L-C-R circuit in an AC circuit is 
(a) 
LC
R (X X ) ?? (b) 
22
LC
R (X X ) ??  (c) R    (d) None of these 
Q 8.  If V
0
 and I
0
 are the peak current and voltage across the resistor in a series L-C-R circuit, then the 
power dissipated in the circuit is 
 (a) 
00
VI
2
   (b) 
00
VI
2
   (c) V
0
I
0
 cos ?   (d) 
00
VI
cos
2
? 
Q 9.  A generator produces a time varying voltage given by V = 240 sin 1201, where t is in second. The 
rms voltage and frequency are 
  (a) 170 V and 19 Hz  (b) 240 V and 60 Hz  (c) 170 V and 60 Hz  (d) 120 V and 19 Hz 
Q 10.  An L-C-R series circuit has a maximum current of 5 A. If L= 0.5H and C = 8 ?F, then the angular 
frequency of AC voltage is 
  (a) 500rad/s   (b) 5000rad/s  (c) 400 rad/s   (d) 250 rad/s 
Q 11.  The current and voltage functions in an AC circuit are 
   i = 100 sin 100/mA, V =100sin 100t V
3
? ??
?
??
??
 
  The power dissipated in the circuit is 
  (a) 10W   (b) 2.5 W   (c) 5 W   (d) 5 kW 
Q 12.  A capacitor becomes a perfect insulator for 
  (a) alternating current (b) direct current  (c) both (a) and (b)  (d) None of these 
Q 13.  For an alternating voltage V = 10 cos 100 ?t volt, the instantaneous voltage at 
1
t
600
? s is 
  (a) 1 V   (b) 5 V   (c) 5 3V   (d) 10 V 
Q 14.  In a purely resistive AC circuit 
  (a) voltage leads current    (b) voltage lags current 
  (c) voltage and current are in same phase  (d) nothing can be said 
Q 15.  Identify the graph which correctly represents the variation of capacitive reactance X
C
 with 
frequency 
  (a)   (b)  (c)  (d) 
Q 16.  In an AC circuit, the impedance is 3 times the reactance, then the phase angle is 
  (a) 60°   (b) 30°   (c) zero   (d) None of these 
Q 17.  Voltage applied to an AC circuit and current flowing in it is given by 
   V 200 2 sin t and i 2 cos t
44
?? ? ? ? ?
? ? ? ? ? ? ?
? ? ? ?
? ? ? ?
 
  Then power consumed in the circuit will be 
  (a) 200 W   (b) 400 W   (c) 200 2W   (d) None of these 
Q 18.  When 100 volt DC source is applied across a coil, a current of 1 A flows through it. When 100 V 
AC source of 50 Hz is applied to the same coil, only 0.5 A current flows. Calculate the inductance 
of the coil 
 (a) ( ?/ 3 )H  (b) ( 3 / ?)H  (c) (2/ ?)H   (d) None of these 
Q 19.  In the circuit shown in figure, the reading of the AC ammeter is