STPM Physics Chapter 18 Alternating Current Circuits

STPM PHYSICS CHAPTER 18 ALTERNATING CURRENT CIRCUITS

SMK SACRED HEART, SIBU

1. Circuit with alternating current: Characteristics Purely resistive circuit (R-circuit) a) Circuit

b) Voltage c) Current

V = Vo sin

, Vo = peak voltage

I= = I = Io sin

Purely inductive circuit (L-circuit)

V = Vo sin

, Vo = peak voltage To maintain I in inductor, V across inductor is V = -E Vsupply Vo sin

= =

Vinductor -E , E=

=

L

Purely capacitive circuit (C-circuit)

V = Vo sin

, Vo = peak voltage For a.c. circuit, rate of charges are conserved. Q=CV = I I

= =

∫ I

=

I

= =

d) Peak current, Io e) Resistance / Reactance

Io =

Io =

XR = R

XL =

f)

From I = Io sin I2 = sin2

Ir.m.s. (Same as Vrms)

Mean square value of sin2 =

,

= Ir.m.s. = g) Phase difference h) Instantaneous power i)

j)

Maximum power

Mean power

P = IV = (Io sin ) (Vo sin = Io Vo sin2 P = I2R = (Io sin )2 R = R sin P = Po sin

=2

=

Io =

CVo =

Xc =

=

= = =

CVo cos Io cos Io sin (

From XL =

From Xc =

Irms =

Irms =

=

==

, = Vrms

From P =

R sin

= 90o P = IV = (Io cos ) (Vo sin = Io Vo sin

)

Io =

P o = I o Vo

P o = I o Vo

Po = R P o = I o Vo

Po =

Po =

Po =

,

Mean square value of sin

(let direction of I lies on X-axis)

=

P = IV = (Io cos ) (Vo sin = Io Vo sin

)

P = Vrms Irms =( )( ) √

=

=

Phasor diagram

C

Io cos Io sin (

= 90o

=

l)

C

=

√

= 0o

P=

k) Leading quantity

∫

=

2

=

Both are in the same phase

√

R

R

Po =

Po =

P=0 (No heat dissipated)

P=0 (no heat dissipated)

Energy stored, U = LI2 = L (Io sin

Mean energy = 0 Peak energy, Uo = L

)

Energy stored, U = CV2 )

2

= C (Vo sin

Mean energy = 0 Peak energy, Uo = C

Voltage Current From “CIVIL”, Capacitor = I leading V ; V leading I = Inductor (L)

)2

STPM PHYSICS CHAPTER 18 ALTERNATING CURRENT CIRCUITS

SMK SACRED HEART, SIBU

2. Circuit with alternating current: Characteristics R-C circuit in series a) Circuit

R-L circuit in series

R-L-C circuit in series

b) Phasor diagram (let direction of I lies on X-axis)

c)

Voltage

V = Vo sin

, Vo = peak voltage

V = Vo sin

, Vo = peak

V = Vo sin

, Vo = peak voltage

voltage

d) Impedance, Z

VR = IR Vc =IXc Vz = IZ

VR = IR VL =IXL Vz = IZ

VR = IR VL =IXL Vz = IZ

Vz = √ IZ = √ Z=√

Vz = √ IZ = √ Z=√ =√

Vz = √ IZ = √ Z=√

=√

=√

= e)

Current

f)

Phase difference

I = Io sin ( = tan-1 ( ) = tan-1 ( ) -1

= tan g) Leading quantity by h) Resonance frequency

3.

4.

5.

(

=

=

I = Io sin (

I = Io sin (

= tan-1 ( ) = tan-1 ( ) -1

)

= tan

Current

Voltage

Nil

Nil

Alternating current Current in which the direction of the current changes or reverses periodically. Direct current Current in which the direction of the current is always the same Peak value Maximum value or amplitude of the alternating current

6.

7.

Vc = IXc

(

= tan-1 (

)

Root-mean-square value of an a.c. The value of a constanct direct current which can produce the same heating power as the alternating current in a given resistor. Phasor A phasor is a vector of constant magnitude and rotating in an anticlockwise direction with a constant angular velocity

= tan-1 ( Nil

) = tan-1 (

)

)

Impedance Z is minimum when f = fr or when XL = Xc

8.

Reactance Opposition to the current by an inductor or a capacitor in an a.c. circuit 9. Impedance The vector sum of the resistance and the reactance in an a.c. circuit 10. Mean power Rate of heat dissipation 11. Instantaneous power Power at a particular moment of time