Sinusoidal Response of RLC Circuits


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1 Sinusoidal Response of RLC Circuits Series RL circuit Series RC circuit Series RLC circuit Parallel RL circuit Parallel RC circuit
2 RL Series Circuit
3 RL Series Circuit
4 RL Series Circuit Instantaneous power Average Power
5 RL Series Circuit Impedance Triangle
6 RL Series Circuit Voltage, current and power waveforms in RL circuit:
7 RC Series Circuit
8 RC Series Circuit
9 RC Series Circuit Average Power Impedance triangle
10 Series RLC Circuit By Kirchhoff s Law ) 1 ( 1 j ] j [ ji C L j R C L j R Z IZ C X L jx R I C X L jix IR V V V
11 Series RLC Circuit Z R 1 j( L ) C
12 Series RLC Circuit From Phasor
13 Series RLC Circuit When X L >X C The phase angle is positive and the circuit is more inductive than capacitive. When X L <X C The phase angle is negative and the circuit is more capacitive than inductive When X L =X C The phase angle = 0 and the circuit is purely resistive
14 Series RLC Circuit Average Power
15 Summary of Circuit Elements, Impedance, Phase Angles
16 Power in AC Circuits Instantaneous Power Product of the voltage and the current at that instant, i.e. instantaneous value of power = vi watts. Average Power Average power over complete cycle P = VI cos φ
17 Power in AC Circuits Active Power or Real power or True power average power over the complete cycle P = VI cos φ watts P = I 2 R Reactive Power Reactive power Q = VI sin φ VAR Apparent Power product of the voltage and the current in an a.c. circuit S = VI voltampere (VA) S 2 = P 2 + Q 2
18 Power in AC Circuits
19 Example #1 A capacitor which has an internal resistance of 10Ω and a capacitance value of 100uF is connected to a supply voltage given as V (t) = 100 sin (314t). Calculate the current flowing into the capacitor. Also construct a voltage triangle showing the individual voltage drops. Solution I = 2.14 A
20 Example #2 A coil having a resistance of 7Ω and an inductance of 31.8mH is connected to 230V, 50Hz supply. Calculate (i) the circuit current (ii) phase angle (iii) power factor (iv) power consumed
21 Example #3 A Capacitor of capacitance 79.5μF is connected in series with a non inductive resistance of 30Ω across a 100V, 50Hz supply. Find (i) impedance (ii) current (iii) phase angle (iv) Equation for the instantaneous value of current
22 Example #4 A 230 V, 50 Hz ac supply is applied to a coil of 0.06 H inductance and 2.5Ω resistance connected in series with a 6.8 μf capacitor. Calculate (i) Impedance (ii) Current (iii) Phase angle between current and voltage (iv) power factor (v) power consumed
23 Parallel RL Circuit Each branch of the circuit can be analysed separately as a series circuit and then the effect of the separate branches can be combined by applying Kirchhoff s law I = I R + I L
24 Parallel RL Circuit From phasor diagram the phase angle is:
25 Parallel RC Circuit I = I R + I C
26 Parallel RC Circuit From phasor diagram the phase angle is:
27 Parallel RLC Circuit I = I R + I L  I C
28 Example #5 A 1kΩ resistor, a 142mH coil and a 160uF capacitor are all connected in parallel across a 240V, 60Hz supply. Calculate the impedance of the parallel RLC circuit and the current drawn from the supply.
29 Example #6 A 50Ω resistor, a 20mH coil and a 5uF capacitor are all connected in parallel across a 50V, 100Hz supply. Calculate the total current drawn from the supply, the current for each branch, the total impedance of the circuit and the phase angle.
30 Example #6
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