Q: To an ac power supply of 220 V at 50 Hz , a resistor of 20 , a capacitor of reactance 25 and an inductor of reactance 45 are connected is series. The corresponding current in the circuit and the phase

aligned & X _ C =25 \\ & X _ L =45 \\ & Z = R ^2+ ( X _ L - X _ C )^2 \\ & Z = 20^2+(45-25)^2 \\ & Z =20 2 aligned aligned & I_ r m s = V_ r m s Z = 220 20 2 = 11 2 =7.8 ~A \\ & = X_L-X_C R = 45-25 20 = 20 20 =1 \\ & =45^ aligned

Question 1

An ac circuit contains a resistance of 1 k , a capacitor of 0.1\ F and an inductor of 1 mH connected in series. The resonance frequency of the circuit is approximately :

Accepted Answer

Given L = 1 mH = 10^ -3 H and C = 0.1\ F = 10^ -7 F . The resonance frequency of a series RLC circuit is given by f_r = 1 2 LC . Substituting the values: f_r = 1 2 10^ -3 10^ -7 f_r = 1 2 10^ -10 f_r = 10^5 2 Hz f_r = 50 kHz 15.9 kHz Answer: 15.9 kHz

Question 2

The peak value of an alternating current is 5 A and frequency is 60 Hz. How long will the current, starting from zero, take to reach the peak value ?

Accepted Answer

The alternating current is given by I = I_0 ( t). The time taken to reach the peak value from zero corresponds to a phase angle of 2 . t = 2 2 f t = 2 t = 1 4f Given f = 60 Hz, we get: t = 1 4 60 = 1 240 s. Answer: 1 240 s

Question 3

An ac voltage V=220 (2 10^3 t) Volt is applied to a series LCR circuit. Then the current amplitude in this circuit is : (Given : L=10 mH, C=25\, , R=100\, )

Accepted Answer

Given V = 220 (2 10^3 t) V, the peak voltage is V_m = 220 V and the angular frequency is = 2 10^3 rad/s. The inductive reactance is X_L = L = (2 10^3) (10 10^ -3 ) = 20 \, . The capacitive reactance is X_C = 1 C = 1 (2 10^3) (25 10^ -6 ) = 1 50 10^ -3 = 20 \, . Since X_L = X_C, the circuit is in resonance. The impedance of the circuit is Z = R^2 + (X_L - X_C)^2 = R = 100 \, . The current amplitude is I_m = V_m Z = 220 100 = 2.2 A. Answer: 2.2 A

Question 4

To an ac power supply of 220 V at 50 Hz , a resistor of 20 , a capacitor of reactance 25 and an inductor of reactance 45 are connected is series. The corresponding current in the circuit and the phase

Accepted Answer

aligned & X _ C =25 \ & X _ L =45 \ & Z = R ^2+ ( X _ L - X _ C )^2 \ & Z = 20^2+(45-25)^2 \ & Z =20 2 aligned aligned & I_ r m s = V_ r m s Z = 220 20 2 = 11 2 =7.8 ~A \ & = X_L-X_C R = 45-25 20 = 20 20 =1 \ & =45^ aligned

Question 5

A step up transformer is connected to an ac mains supply of 220 V to operate at 11000 ~V , 88 watt. The current in the secondary circuit, ignoring the power loss in the transformer, is

Accepted Answer

In secondary circuit, P=V i 88=11000 i i= 88 11 10^3 =8 10^ -3 ~A i=8 ~mA

Question 6

The amplitude of the charge oscillating in a circuit decreases exponentially as Q=Q_0 e^ -R t 2 L , where Q_0 is the charge at t=0 ~s . The time at which charge amplitude decreases to 0.50 Q_0 is near

Accepted Answer

Given Q=Q_0 e^ -R t / 2 L R=1.5 , L=12 mH , In (2)=0.693 Q=0.5 Q_0, t= ? 0.5 Q_0=Q_0 e^ -R t / 2 L 1 2 =e^ -R t / 2 L Taking log on both sides ( 1 2 )= e^ -R t / 2 L 2= R t 2 L t= 2 L In 2 R = 2 12 10^ -3 0.693 1.5 t=11.09 ~ms

Question 7

In the circuit shown below, the inductance L is connected to an ac source. The current flowing in the circuit is I=I_0 t. The voltage drop (V_L ) across L is

Accepted Answer

V_L leads current / by 2 V_L=V_0 ( t+ 2 ) ( I=I_0 t ) V_0=I_0 X_L V_L=10 X_L ( t)=10 L ( t)

Question 8

A 10 F capacitor is connected to a 210 ~V , 50 ~Hz source as shown in figure. The peak current in the circuit is nearly ( =3.14) :

Accepted Answer

Capacitive Reactance aligned X_C & = 1 C = 1 2 f C = 1 2 3.14 50 10 10^ -6 \ & = 1000 3.14 aligned aligned & V_ rms =210 ~V \ & i_ rms = V_ rms X_C = 210 X_C aligned aligned Peak current & = 2 i_ ms = 2 210 1000 3.14=0.932 \ & 0.93 ~A aligned

Question 9

In an ideal transformer, the turns ratio is N_P N_S = 1 2 . The ratio V_S: V_P is equal to (the symbols carry their usual meaning) :

Accepted Answer

According to transformer ratio, V_S V_P = N_S N_P =2: 1

Alternating Current — Previous Year Questions & Solutions