Answer.2. Less than

A series RLC circuit contains resistance, inductance, and capacitance. Since inductive reactance and capacitive reactance have opposite effects on the circuit phase angle, the total reactance is less than either individual reactance.

Answer.1. Zero

Explanation:-

As we know that, inductive reactance (X_L) causes the total current to lag the applied voltage. Capacitive reactance ( (X_C) has the opposite effect. It causes the current to lead the voltage. Thus X_L and X_C tend to offset each other. When they are equal, they cancel, and the total reactance is zero.

Answer.3. Equal in

Explanation:-

Resonance is a condition in a series RLC circuit in which the capacitive and inductive reactances are equal in magnitudes.

Answer.4. Increase

Explanation:-

The resonant frequency in the series RLC circuit is,

$\begin{array}{l} {f_r} = \frac{1}{{2\pi \sqrt {LC} }}\\ \\ {f_r} \propto \frac{1}{{\sqrt C }} \end{array}$

From the above equation, the resonant frequency of the series RLC circuit is inversely proportional to the square root of the capacitance.
By the above equation, the value of the capacitance C in a series RLC circuit is decreased, then the resonant frequency in a series RLC circuit is increased.

Answer.1. Decrease

Explanation:-

Q factor or quality factor of RLC circuit is given as

Q = F_r​/​B_w

B_w ​ = Bandwidth

F_r = Resonance Frequency

From the above equation, it is clear that the quality factor is inversely proportional to the bandwidth hence as Q increases, bandwidth​ decreases.

Answer.2. 18,780 Ω

It is for internal resistance present in the inductor and capacitor.

Genrally, we solve this problem in tank circuit model
XL=2*3.14*f*L.
Xc=1/(2*3.14*f*C).

After convert all parallel networks into conductance,s uceptance, admitance values
Conductance(G)=(R)/(R^2 + X^2); R=30
In this scenario internal restance present in L&C.
so we are taking suceptance(B)=(X)/(R^2 + X^2); R=30.
Y=y1 + y2 + y3 Here, Y= admitance.

Y=G1+G2 + G3 + J(BL -Bc); G1 value take restor R1=6800 OHM; G2&G3 values take R=30.

After calculation,
Y=G + J(B),
finally R=1/G,
R=18,780 OHMS.

Answer.3. X_tot = |X_L − X_C|

Explanation:-

Inductive reactance (X_L) causes the total current to lag the applied voltage. Capacitive reactance ( (X_C) has the opposite effect. It causes the current to lead the voltage.

The magnitude of the total reactance in the series circuit is

X_tot = |X_L − X_C|

The term |X_L − X_C| means the absolute value of the difference of the two reactances. That is, the sign of the result is considered positive no matter which reactance is greater. For example, 5 − 8 = − 3, but the absolute value is

|5 − 8| = 3

Answer.2. Inductive in nature

Explanation:-

The phase difference (φ) is the angle by which the current drawn from the supply lags or leads the applied voltage in a series RLC circuit. When the inductive reactance is greater than the capacitive reactance the circuit is inductive and the current lags the voltage.

The phasor diagram represents the voltages in the circuit in relation to the current (I) that is the reference phasor. The current (I) is in phase with V_R  leads V_C by 90°. The applied voltage (V) is determined by resolving V_L and V_C. For inductive load, the applied voltage is (V_L — V_C).

Answer.1. Capacitive in nature

Explanation:-

When the capacitive reactance is greater than the inductive reactance the circuit is capacitive and the current leads the voltage. The current (I) is in phase with V_R  lags V_L by 90°. The applied voltage (V) is determined by resolving V_L and V_C. For capacitive load, the applied voltage is (V_C — V_L).

Answer.4. Z = R +( jX_L − JX_C)

Explanation:-

The impedance of the RLC circuit in rectangular form is given as

Z = R +( jX_L − JX_C)

Where

X_L = Inductive Reactance

X_C = Capacitive reactance

R = Resistance