The combined opposition to the flow of current in a series RLC circuit is called impedance (symbol Z). The combined values of resistance, inductive reactance and capacitive Reactance can be represented in the form of an impedance triangle as in Figure
The magnitude in a series RLC circuit is the difference of the two reactance i.e capacitive reactance and inductive reactance and it is given as
$Z = \sqrt {{R^2} + ({X^2}L – {X^2}_C)} $
11. The phase angle between the total current and applied voltage of the series RLC circuit is
tan−1(R/XC)
tan−1(R/Xt)
tan−1(Xt/R)
±tan−1(Xt/R)
Answer.4. ±tan−1(Xt/R)
Explanation:-
The phase difference 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. When the capacitive reactance is greater than the inductive reactance the circuit is capacitive and the current leads the voltage.
The phase difference is calculated by applying the trigonometry ratios of sine, cosine or tangent to the voltage phasor diagram or the impedance triangle. In many problems the tangent ratio is used:
±tan−1(Xt/R)
If the circuit is predominately inductive, the phase angle is positive; and if predominately capacitive, the phase angle is negative.
12. In the series RLC circuit, the capacitive reactance is 3.39 kΩ, Inductive reactance is 6.28 kΩ and the resistance is 5.6 kΩ. The magnitude of the total reactance is
2.89 Capacitive
2.89 Inductive
2.89 Resistive
None of the above
Answer.2. 2.89 Inductive
Explanation:-
Given
XL = 6.28 kΩ
XC = 3.39 kΩ
In this case, XL is greater than XC and thus the circuit is more inductive than capacitive. The magnitude of the total reactance is
The magnitude of the total reactance in the series circuit is
Xtot = |XL − XC|
Xtot = |6.28 − j3.39|
Xtot = 2.89 Inductive
13. In the series RLC circuit, the capacitive reactance is 3.39 kΩ, Inductive reactance is 6.28 kΩ and the resistance is 5.6 kΩ. The magnitude of the total impedance is
8.48Ω
7.52Ω
3.39Ω
6.30Ω
Answer.4. 6.30Ω
Explanation:-
Given
XL = 6.28 kΩ
XC = 3.39 kΩ
R = 5.6 kΩ
Xtot = |XL − XC|
Xtot = |6.28 − j3.39|
Xtot = 2.89
The magnitude in a series RLC circuit is given as
$\begin{array}{l} Z = \sqrt {{R^2} + ({X^2}_{Tot})} \\ \\ \\ Z = \sqrt {{{(5.6)}^2} + {{(2.89)}^2}} \end{array}$
Z = 6.30Ω
14. A series RLC circuit has the voltages VR = 20 V, VL = 30 V and VC = 50 V across the circuit components Calculate the applied voltage.
282.8 V
2.828 V
28.28 V
0.282 V
Answer.3. 28.28 V
Explanation:-
The voltage in series RLC series circuit is given by the expression
15. Determine the voltage in the series RLC circuit when the R = 800Ω, I = 200 mA L = 32 mH, F = 200 Hz and C = 8μF.
R = 160 V, VL = 8.04 V, VC = 19.9 V
R = 8.04 V, VL = 160 V, VC = 19.9 V
R = 19.9 V, VL = 160 V, VC = 8.04 V
R = 8.04 V, VL = 160 V, VC = 10.9 V
Answer.1. R = 160 V, VL = 8.04 V, VC = 19.9 V
Explanation:-
Given
Resistance R = 800Ω
Inductance L = 32 mH = 0.032H
Capacitance C = 8μF = 8 × 10−6
Current I = 200 mA = 0.2 A
Resitance voltage
VR = I.R = 0.2 × 800
VR = 160 V
Capacitance reactance
XC = 1/2πfc
= 1/6.28 × 200 × 8 × 10−6
XC = 99.5Ω
Capacitance Voltage
VC = I.XC = 0.2 × 99.5
VC = 19.9 V
Inductive Reactacne
XL = 2πfL
= 6.28 × 200 ×0.032
XL = 40.2Ω
Inductance Voltage
VL = I.XL = 0.2 × 40.2
VL = 8.04 V
16. In series RLC circuit when inductive reactance is equal to the capacitive reactance the circuit is _____
Lagging
Leading
Resonance
None of the above
Answer.3. Resonance
Explanation:-
Resonance is a condition in a series RLC circuit in which the capacitive and inductive reactances are equal in magnitude; thus, they cancel each other and result in a purely resistive impedance. In a series RLC circuit, the total impedance was given in
Z = R + jXL − jXC
At resonance, XC = XLand the j terms cancel; thus, the impedance is purely resistive. These resonant conditions are stated in the following equations:
XC = XL
Zr = R
In a series RLC circuit, series resonance occurs when capacitive reactance is XC = XL. The frequency at which resonance occurs is called the resonant frequency and is designated by fr.
17. During resonance condition in series RLC circuit, the Inductor voltage VL and capacitance Voltage VC are _______ out of phase.
90°
180°
0°
45°
Answer.2.180°
Explanation:-
In the resonance condition an RLC series circuit is equal to unity since the impedance is purely resistive, In this condition, the maximum power is transferred to the circuit. In this situation, the current in the circuit must be at a maximum because the impedance is at its minimum. This occurs at a unique frequency when the inductive and capacitive reactances effectively cancel each other that is, they are equal in magnitude and 180° out of phase.
Thus during resonance conditions in the series RLC circuit the Inductor voltage VL and capacitance Voltage VC are 180° out of phase.
18. In a series RLC circuit during resonance, the resonant frequency is given by
(1) ${f_r} = \sqrt {\frac{L}{{2C}}} $
(2) ${f_r} = \sqrt {\frac{L}{C}} $
(3) ${f_r} = \frac{1}{{2\sqrt {LC} }}$
(4) ${f_r} = \frac{1}{{2\pi \sqrt {LC} }}$
Answer.4. ${f_r} = \frac{1}{{2\pi \sqrt {LC} }}$
Explanation:-
For a given series RLC circuit, resonance occurs at only one specific frequency. A formula for this resonant frequency is developed as follows:
XL = XC
where
XC = 1/2πfrC
XL = 2πfrL
Substitute the reactance formula
2πfrL = 1/2πfrC
Multiplying both sides by fr/2πL
$f_r^2 = \dfrac{1}{{4{\pi ^2}LC}}$
Take the square root of both sides. The formula for series resonant frequency is
${f_r} = \frac{1}{{2\pi \sqrt {LC} }}$
19. At the series resonant frequency, the current is ______
Minimum
Maximum
Zero
Infinite
Answer.2. Maximum
Explanation:-
In series RLC circuit current, I = V / Z but at resonance condition current is I = V/R since inductive and capacitive reactances effectively cancel each other. At the resonant frequency, the capacitive reactance is equal to inductive reactance, and hence the impedance is minimum. Because of minimum impedance, maximum current flows through the circuit.
20. Series Resonant circuit is also called as______
Donor circuit
Power circuit
Zero circuit
Acceptor circuit
Answer.4. Acceptor circuit
Explanation:-
We know that in a series resonant circuit, the current has maximum value and impedance has a minimum value. So the series resonant circuit is called an accepter circuit because due to minimum impedance it accepts all frequencies close to the resonant frequency.