2018-10-01_Physics_For_You

ALTERNATING CURRENT

It is the current which varies continuously in magnitude
and periodically in direction. It can be represented by
I = I 0 sinZt or I = I 0 cosZt.
where I 0 is peak value of current and is known as
amplitude of ac and I is the instantaneous value of ac.

ω==^2 π 2 πυ

T

where T is period of ac and X is frequency

of ac.
Voltages and currents that vary symmetrically in
magnitude and direction with time are very common.
e electric mains supply in our homes and oces is a
voltage that varies like a sine function with time. Such
a voltage is called alternating voltage (ac voltage) and
the current driven through the appliances is called the
alternating current (ac current)

Average Values of AC Voltage and AC
Current
AC voltage or current are commonly sinusoidal (sine
or cosine function) and their mean values for complete
cycle is zero. e average values for half cycles are
equally positive and negative

• Average value for one half cycle (or rectied
  average value)
  V = V 0 sin Zt

∴= ==

∫

∫

() ..

/

V /

Vdt

dt

VV

T

av T

0

2

0

2 00

2

0 637

π

is is also known as the rectied average value of a

sinusoidal voltage and is represented as Vav.

• Root Mean Square Value (Vrms or Irms)
  Since V or I are equally negative and positive, their
  squares will always be positive and the square root
  of the average of their square will give the rms
  values.
  ? V = V 0 sinZt

()V sin(cos)

T

Vtdt

V

T

tdt

2 TTV

0

(^22)
0
0
2
0
2
0
1
2
12
av 2
==∫∫ωω−=
us VVrmsa==()^2 v V^0
2
and II

I

rmsa==()v

2 0

2

or RMS value=Peak value

2

SERIES AC CIRCUITS

When only Resistance is in AC Circuit

Consider a simple ac circuit

consisting of a resistor of

resistance R and an ac generator,

as shown in gure.

According to Kirchho ’s loop law

at any instant, the algebraic sum

of the potential dierence around a closed loop in a

circuit must be zero.

H – VR = 0 ; H – IRR = 0 ; H 0 sinZt – IRR = 0

I

R

R==tI t

ε

(^0) sinsωω 0 in ...(i)
where I 0 is the maximum current, I
(^0) R
=ε^0
From above equations, we see that the instantaneous
voltage drop across the resistor is
VR = I 0 RsinZt ...(ii)

• Phasor Diagram : We see
  in equation (i) and (ii), IR
  and VR both vary as sinZt
  and reach their maximum
  values at the same time
  as shown in gure (a),
  they are said to be in
  phase. A phasor diagram
  is used to represent phase
  relationships. e lengths
  of the arrows correspond to
  V 0 and I 0. e projections
  of the arrows onto the
  vertical axis gives VR and IR.
  In case of the single-loop resistive circuit, the current
  and voltage phasors lie along the same line, as shown
  in gure (b), because IR and VR are in phase.

When only Inductor is in an AC Circuit

Now consider an ac circuit

consisting only of an inductor of

inductance L connected to the

terminals of an ac generator, as

shown in the gure.

e induced emf across the inductor is given by L

dI

dt

.

On applying Kirchho ’s loop rule to the circuit

H – VL = 0 ⇒ ε−L =

dI

dt

(^0)
When we rearrange this equation and substitute H = H 0
sinZt, we get