1) The document discusses resistive circuits and resistance. It defines resistance as a property that opposes current flow and defines the relationship between voltage, current, and resistance using Ohm's Law. 2) It also discusses conductance, resistivity, and how a material's resistance changes with temperature based on its temperature coefficient. Common temperature coefficients and resistivities for various materials are provided. 3) Formulas are provided for calculating equivalent resistance for resistors in series and parallel configurations, as well as equations for calculating current division in parallel circuits. Worked examples of resistive circuit problems are also included.

1. Resistive Circuits

2. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 2
Resistors
Resistance
Property which opposes the flow of current
R = V/I
Unit – Ohms (Ω)
Power P = VI = V2
/R = I2
R
Conductance
Reciprocal of resistance
Symbol: G
Unit – Siemens (S)
R
V
I

3. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 3
Problem - 1

4. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 4
Problem - 2

5. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 5
Resistivity & Temperature Coefficient
( )
( )
( )20
10
2
1
0
1001
1
1
Where
1
θα
θα
α
θα
+
+
=
+=
R
R
RR
For a homogeneous material
Where
= resistivity
a = cross sectional area of the Resistor
l = length of the Resistor
ρ
= Temperature coefficient of R at 0o
a
l
R ρ=

6. 0
R
R1
R0
R2
θ1 θ2
θ
Variation of Resistance of Copper with Temperature
ELE 101 / 102 Dept of E & E Engg, MIT Manipal 6
Resistivity & Temperature Coefficient
Super Conductivity !
( )1001 1 θα+= RR

7. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 7
Temperature Coefficients
of Resistivity
Material Temperat
ure
Coefficien
t °C-1
@
0° C
Aluminum 0.00381
Copper 0.00428
Gold 0.0034
Tungsten 0.0045
Brass 0.001
Manganin 0.00002
Carbon (graphite) -0.00048
Germanium (pure) -0.048
Silicon (pure) -0.075
Material at 0° C
Aluminium 2.7 * 10 -8
Copper 1.59 * 10 -8
Tungsten 5.35 *10 -8
Carbon 6500 * 10 -8
Manganin 42 * 10 -8
ρ
Resistivity:
Resistivity & Temperature Coefficient

8. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 8
Problem- 3
When a potential difference of 10 V is applied to a coil of copper wire of
mean temperature 20° C, a current of 1.0 A flows in the coil. After some
time the current falls to 0.95 A yet the supply voltage remains unaltered.
Determine the mean temperature of the coil given that the temperature
coefficient of resistance of copper is 4.28 * 10-3
/°C referred to 0° C.
[33.5 o
C]

9. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 9
Resistive circuits
Resistors in series:
Resistors in parallel:
R1R2
R3
321
1111
RRRReq
++=

10. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 10
Parallel Resistive circuits
Current Division in Parallel Circuits
( )
1 2
1 21
1 1 1
2 2
2
1
1 2
1
2
1 2
I I I
R RR
I I I
R R
R
I I
R R
R
I I
R R
= +
+
= + =
=
+
=
+