sinusoidal response of rlc...

Department of Electrical & Electronics Engineering, Amrita Vishwa Vidyapeetham, Coimbatore.

Sinusoidal Response of RLC Circuits

Series RL circuit

Series RC circuit

Series RLC circuit

Parallel RL circuit

Parallel RC circuit


R-L Series Circuit


R-L Series Circuit

Instantaneous power

Average Power


R-L Series Circuit

Impedance Triangle


R-L Series Circuit

Voltage, current and power waveforms in RL circuit:


R-C Series Circuit


R-C Series Circuit

Average Power

Impedance triangle


Series RLC Circuit

By Kirchhoff’s Law

)1

(1

j

]j[

jI

CLjR

CLjRZ

IZ

CX

LjXRI

CX

LjIXIR

V

V

V


Series RLC Circuit

)1

(C

LjRZ


Series RLC Circuit

From Phasor


Series RLC Circuit

When XL>XC

The phase angle is positive and the circuit is

more inductive than capacitive .

When XL<XC

The phase angle is negative and the circuit is

more capacitive than inductive

When XL=XC

The phase angle = 0 and the circuit is purely

resistive


Series RLC Circuit

Average Power


Summary of Circuit Elements, Impedance, Phase Angles


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



Active Power or Real power or True power

average power over the complete cycle

P = VI cos φ watts

P = I2R

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 volt-ampere (VA)

S2 = P2 + Q2


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


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


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


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


Parallel R-L 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 = IR + IL


Parallel R-L Circuit

From phasor diagram the phase angle is:


Parallel R-C Circuit

I = IR + IC


Parallel R-C Circuit

From phasor diagram the phase angle is:


Parallel RLC Circuit

I = IR + IL - IC


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.


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.


Example #6

sinusoidal response of rlc...

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