Test: AC Voltage Applied to an Inductor, Capacitor & Series LCR Circuit (February 4) - NEET MCQ

Capacitive reactance (symbol XC) is a measure of a capacitor’s opposition to AC (alternating current). Like resistance it is measured in ohms, but reactance is more complex than resistance because its value depends on the frequency (f) of the signal passing through the capacitor. Reactance is also inversely proportional to the value of capacitance (C), i.e. the value of XC at any frequency will be less in larger capacitors than in smaller ones. All capacitors have infinitely high values of reactance at 0Hz, but in large capacitors, the reactance falls to a low level at much lower frequencies than in smaller capacitors. Hence, larger capacitors are preferred in low frequency applications.

In pure inductance circuit, R=0
Thus power factor of pure inductance circuit cosϕ=R/Z​=0
Average power dissipation P_av​=V_rms​I_rms​cosϕ
⟹ P_av​=0

equation of alternating voltage , E = 200√2sin(100t)
compare this equation with E₀sin(ωt)
so,  E₀=200√2 volts
ω= 100 rad/s
now, E_rms=E₀/√2
= 200√2/√2 = 200 volts .
given, capacitance of capacitor, C = 10^-6 F
so, reactance of capacitor,  X_C=1/ω_C
=1/(10^-6x100)
=10⁴
so, the reading of Ammeter, I=E_rms/X_C
= 200/10⁴ A = 20 × 10^-3 A = 20mA
hence, option (b) is correct.

Voltage lags current by 90° in a pure capacitive circuit. In a pure capacitive circuit, the instantaneous power may be positive or negative. As with the simple inductor circuit, the 90-degree phase shift between voltage and current results in a power wave that alternates equally between positive and negative.

Q-factor: In LCR Circuit, the ratio of resonance frequency to the difference of its neighbouring frequencies so that their corresponding current is 1/√2​ times of the peak value, is called Q-factor of the circuit.
Formula: Q=(1/R)​ √(L/C)​​
So, Q ∝1/R
Conditions for the large value of Q factor:
(i) Value of CL​ should be large.
(ii) Value of R should be less.
 

P(t)=V_mI_mSin²ωt
P(t)=0.5V_mI_m(2sin2ωt)
P(t)= 0.5V_mI_m(1-cos2ωt)
Therefore, frequency is doubled for the instantaneous power so, frequency of instantaneous power is 100Hz.
 

As we know,
Average power in ac circuit is given by P=V_rms​i_rms​cosϕ 
For pure capacitive circuit ϕ=90^o so P=0

In a.c. circuits, a choke coil is used to control the current in place of a resistance. If a resistance is used to control the current, the electrical energy will be wasted in the form of heat. Due to its inductive reactance, a choke coil decreases the current without wasting electrical energy in the form of heat.