1) The document discusses power in RC circuits and how power is dissipated by resistance as heat or stored by capacitors. It provides formulas to calculate active power, reactive power, and apparent power. 2) A RC circuit can function as an oscillator if the resistance value is chosen such that the output voltage leads the input by 60 degrees. The amplifier must have a gain of at least 29 for oscillations to be maintained. 3) RC circuits can also function as filters, either passing low frequencies while blocking high (low-pass) or passing high while blocking low (high-pass), depending on whether the output is taken across the resistor or capacitor. Cutoff frequency determines which frequencies are passed or stopped.

1. ﷽
Presentation
CA
Presentation By: Dr. Maryam Liaqat

2. 1 Ghulfam kokab
Muhammad Adnan
Rab Nawaz
2
3
4
5
6
Sadia Asghar
Khadija yousaf
Maria Allah yar
Group-j MSc. Section-A
Introduction

3. Chapter:15 RC circuit Part 4
SpecialTopics
15-8 Power in RC Circuit
INTRODUCTION
 In RC Circuit all of the energy delivered by the source.
 Resistance dissipate the energy in the form of heat
 Capacitor store energy in 1st Voltage cycle and returned it in 2nd Voltage cycle.
All the energy dissipated is determine by the relative value of R and C

4. PowerinRCCircuit
Conditions
In RC Circuit :
1. if R > C Energy more dissipated
2. if C > R More Energy stored and returned

5. PowerinRCCircuit
It is the Power which is developed in the Circuit Resistance
Its unit is Watt
Active power or Actual Power
Formula
P = V × 𝐼 𝐶𝑜𝑠𝜃
= V × 𝐼 (
𝑅
𝑧
) → P.F = 𝑐𝑜𝑠𝜃 =
𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝐼𝑚𝑝𝑒𝑑𝑒𝑛𝑐𝑒
= (
𝑉
𝑧
) × 𝐼 × R → V= 𝐼 × 𝑍
= 𝐼 × 𝐼 ×R
P = 𝐼2 ×R

6. PowerinRCCircuit
It is the Power which is developed in the Circuit Capacitor
Its unit is VAR ( volt-Ampere-reactive)
Formula
Q = V × 𝐼 𝑆𝑖𝑛𝜃
= V × 𝐼 (
𝑋
𝑧
) P.F = 𝑆𝑖𝑛𝜃 =
𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝐼𝑚𝑝𝑒𝑑𝑒𝑛𝑐𝑒
= (
𝑋
𝑧
) × 𝐼 × Xc
= 𝐼 × 𝐼 × Xc
Q= 𝐼2 × Xc

7. PowerinRCCircuit
 The total power that appears to be transferred between the source and RC circuit.
Its unit is volt-Ampere
Formula
S = V × 𝐼
Power Factor
 P.F is the cosine of the angle b/w Voltage and current.
∅
I
V
P.F = Cos ∅
It is also define as Ratio b/w resistance and impedance
Cos ∅ =
𝑅
𝑧

8. Power Triangle
Power triangle shows the relation between reactive , active and apparent power in the a right
Triangle.
P = V × 𝑰 𝑪𝒐𝒔𝜽
Q=V×𝑰𝑺𝒊𝒏𝜽
Relation
𝒖𝒔𝒊𝒏𝒈 𝑷𝒚𝒕𝒉𝒂𝒈𝒐𝒓𝒂𝒔 𝑻𝒉𝒆𝒐𝒓𝒆𝒎
𝑯𝒚𝒑 𝟐
= 𝒃𝒂𝒔𝒆 𝟐
+ 𝒉𝒊𝒆𝒈𝒉𝒕 𝟐
(𝑽 × 𝑰) 𝟐
= (V × 𝑰 𝑺𝒊𝒏𝜽) 𝟐
+(V × 𝑰 𝒄𝒐𝒔𝜽) 𝟐
𝑺 𝟐
= 𝑷 𝟐
+ 𝑸 𝟐
Taking Square root
S =
1
2 As
𝑩𝒂𝒔𝒆
𝑯𝒚𝒑
= 𝑪𝒐𝒔𝜽
𝑷
𝑺
= 𝑪𝒐𝒔𝜽
Pt = S 𝑪𝒐𝒔𝜽
PowerinRCCircuit

9. BasicApplications
Definition A linear electronic oscillator circuit that produce a Sin wave out put.
It is used to shift the phase through 180 at a certain frequency
Principle The out put voltage V’ across the R leads the input applied Voltage V by some angle ∅
If we Reduce the R to zero then out put voltage leads 𝟗𝟎 𝒐.
Explanation
As In RC Circuit R could not be zero therefore in practice R is
varied to such a Value that makes V’ to lead V by 𝟔𝟎 𝒐. The
Following Circuit diagram show the three sections of the RC
network.

10. Construction 1 Amplifier 2 RC Feed back Network
 The output of the amplifier is phase shifted by the RC network and returned to the
input of the amplifier ,which provides sufficient gain to maintain oscillations. The
gain must be 29.
 The Frequency at which 𝟏𝟖𝟎 𝒐 phase shift occurs is given by the equation
𝒇𝒓 =
𝟏
𝟐𝝅 𝟔 𝑹𝑪

11. BasicApplications
The RC Circuit as a Filter
Filter
Filters are frequency-selection circuits that permit signals of certain frequencies to
pass from the input to the output while blocking all others.
There are Two types of RC Filter.
1
 It can be easily made by connecting together in a
series resistor with a single capacitor.
 In this type Vin is applied to the series
combination but the out put Vout signal is taken
across the capacitor.
Low pass Filter
A low-pass filter (LPF) is a filter that passes signals with a frequency lower than a selected
cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency.
Construction

12. Explanation The Following Fig. shows the filtering action of a series RC circuit using specific
values for illustration.

13. 2
 It can be easily made by connecting together in a
series resistor with a single capacitor.
 In this type Vin is applied to the series
combination but the out put Vout signal is taken
across the Resistor.
High pass Filter
A high-pass filter (HPF) is an electronic filter that passes signals with a frequency higher than a certain
cutoff frequency and attenuates signals with frequencies lower than the cutoff frequency.
Construction
Explanation
The Following Fig. shows the filtering action of a series RC circuit using specific
values for illustration.

14.  Cutoff Frequency (fc) stop or
pass the low or high Frequency
depending on the signal.

15. Prepared by: Ghulfam Kokab
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